PHAS0029-Session06-EulerRungeKutta-Shameer.ipynb

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    "# Numerical solutions to differential equations: The Euler and Runge Kutta methods.\n",
    "\n",
    "_Author: louise.dash@ucl.ac.uk\n",
    "Last updated: 17.02.2021_"
   ]
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    "In this session, we're going to start looking at how to solve differential equations numerically. \n",
    "\n",
    "There are pre-existing python modules that will do this for you - like [scipy.integrate.solve_ivp](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html#scipy.integrate.solve_ivp),\n",
    "but as physicists it's important that you understand exactly how these methods work, so rather than using pre-existing modules as a [black box](http://en.wikipedia.org/wiki/Black_box), we're going to start from the basics.\n",
    "\n",
    "In this session we're going to solve first-order ordinary differential equations of the form\n",
    "\n",
    "$$ \n",
    "\\frac{dx}{dt} = f(x,t)\n",
    "$$\n",
    "\n",
    "to obtain a solution $x(t)$ over some time interval $t_0 \\leq t \\leq t_f$. (We'll come to second-order equations in the next session). We'll start with the simplest approach, [Euler](https://en.wikipedia.org/wiki/Leonhard_Euler)'s method, and refine this until we get to the most useful (and most widely-used) approach, the fourth-order [Runge](https://en.wikipedia.org/wiki/Carl_David_Tolm%C3%A9_Runge)-[Kutta](https://en.wikipedia.org/wiki/Martin_Wilhelm_Kutta) method.\n",
    "\n",
    "\n",
    "If you want to read further on this, then Newman *\"Computational Physics\"*, Chapter 8 section 1 is a great resource, upon which some of the material in this notebook is based.\n",
    "\n",
    "\n",
    "As always, we'll start by importing all the modules we need in this notebook.\n",
    "\n"
   ]
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   "source": [
    "%matplotlib notebook\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "## Euler method"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "Euler's method takes a very simple approach to solving ordinary differential equations. For an equation of the form\n",
    "$$ \n",
    "\\frac{dx}{dt} = f(x,t)\n",
    "$$\n",
    "and a given starting condition for some $t$, we can use a Taylor expansion to solve the equation at a later time $t+ h$:\n",
    "$$\n",
    "x(t+h) = x(t) + h \\frac{{\\rm d} x}{{\\rm d} t} + \\frac{1}{2} h^2 \\frac{{\\rm d}^2 x}{{\\rm d t}^2} + \\ldots \\\\ \n",
    "\\qquad = x(t) + h f(x,t) + {\\rm O}(h^2).\n",
    "$$\n",
    "Euler's method discards all the terms of order $h^2$ and higher, and applies this repeatedly for intervals of size $h$. We start off at $t = t_0$ (usually $t_0 = 0$), and propagate through the $t$-values, incrementing by $h$ each time, until we reach the final value of $t$.\n",
    "\n",
    "\n",
    "Let's see how this works in practice.\n",
    "\n",
    "We'll use it to solve the equation \n",
    "\n",
    "$$ \\frac{ d x}{ d t} = -x^3 + \\sin t,$$\n",
    "\n",
    "to find $x(t)$, with the initial condition of $x = 0$ at $t = 0$. This is a first-order, linear differential equation, but note that it's non-separable.\n",
    "\n",
    "The first thing to do is to write a function that implements the right-hand side of this equation:\n"
   ]
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   "source": [
    "def f(x,t):\n",
    "    ''' Definition of our numerical function\n",
    "    Inputs:\n",
    "    x: a value or array of x values\n",
    "    t: time at which to evaluate the function\n",
    "    Outputs:\n",
    "    f(x,t): function evaluated for this x and t'''\n",
    "    \n",
    "    #return -x**3 + np.sin(t) # our function\n",
    "    return -2*np.exp(-t) # our function\n",
    "\n",
    "    "
   ]
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   "cell_type": "markdown",
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   "source": [
    "In order to find $x(t)$, we need to specify what time interval we want to solve for, and specify the total number of steps we want to use. We can then create an array of $t$-points (time points):"
   ]
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      "Step size h is 0.01\n",
      "[0.   0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1  0.11 0.12 0.13\n",
      " 0.14 0.15 0.16 0.17 0.18 0.19 0.2  0.21 0.22 0.23 0.24 0.25 0.26 0.27\n",
      " 0.28 0.29 0.3  0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4  0.41\n",
      " 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5  0.51 0.52 0.53 0.54 0.55\n",
      " 0.56 0.57 0.58 0.59 0.6  0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69\n",
      " 0.7  0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8  0.81 0.82 0.83\n",
      " 0.84 0.85 0.86 0.87 0.88 0.89 0.9  0.91 0.92 0.93 0.94 0.95 0.96 0.97\n",
      " 0.98 0.99 1.   1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1  1.11\n",
      " 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.2  1.21 1.22 1.23 1.24 1.25\n",
      " 1.26 1.27 1.28 1.29 1.3  1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39\n",
      " 1.4  1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.5  1.51 1.52 1.53\n",
      " 1.54 1.55 1.56 1.57 1.58 1.59 1.6  1.61 1.62 1.63 1.64 1.65 1.66 1.67\n",
      " 1.68 1.69 1.7  1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.8  1.81\n",
      " 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9  1.91 1.92 1.93 1.94 1.95\n",
      " 1.96 1.97 1.98 1.99 2.   2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09\n",
      " 2.1  2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.2  2.21 2.22 2.23\n",
      " 2.24 2.25 2.26 2.27 2.28 2.29 2.3  2.31 2.32 2.33 2.34 2.35 2.36 2.37\n",
      " 2.38 2.39 2.4  2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.5  2.51\n",
      " 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.6  2.61 2.62 2.63 2.64 2.65\n",
      " 2.66 2.67 2.68 2.69 2.7  2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79\n",
      " 2.8  2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.9  2.91 2.92 2.93\n",
      " 2.94 2.95 2.96 2.97 2.98 2.99 3.   3.01 3.02 3.03 3.04 3.05 3.06 3.07\n",
      " 3.08 3.09 3.1  3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.2  3.21\n",
      " 3.22 3.23 3.24 3.25 3.26 3.27 3.28 3.29 3.3  3.31 3.32 3.33 3.34 3.35\n",
      " 3.36 3.37 3.38 3.39 3.4  3.41 3.42 3.43 3.44 3.45 3.46 3.47 3.48 3.49\n",
      " 3.5  3.51 3.52 3.53 3.54 3.55 3.56 3.57 3.58 3.59 3.6  3.61 3.62 3.63\n",
      " 3.64 3.65 3.66 3.67 3.68 3.69 3.7  3.71 3.72 3.73 3.74 3.75 3.76 3.77\n",
      " 3.78 3.79 3.8  3.81 3.82 3.83 3.84 3.85 3.86 3.87 3.88 3.89 3.9  3.91\n",
      " 3.92 3.93 3.94 3.95 3.96 3.97 3.98 3.99 4.   4.01 4.02 4.03 4.04 4.05\n",
      " 4.06 4.07 4.08 4.09 4.1  4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19\n",
      " 4.2  4.21 4.22 4.23 4.24 4.25 4.26 4.27 4.28 4.29 4.3  4.31 4.32 4.33\n",
      " 4.34 4.35 4.36 4.37 4.38 4.39 4.4  4.41 4.42 4.43 4.44 4.45 4.46 4.47\n",
      " 4.48 4.49 4.5  4.51 4.52 4.53 4.54 4.55 4.56 4.57 4.58 4.59 4.6  4.61\n",
      " 4.62 4.63 4.64 4.65 4.66 4.67 4.68 4.69 4.7  4.71 4.72 4.73 4.74 4.75\n",
      " 4.76 4.77 4.78 4.79 4.8  4.81 4.82 4.83 4.84 4.85 4.86 4.87 4.88 4.89\n",
      " 4.9  4.91 4.92 4.93 4.94 4.95 4.96 4.97 4.98 4.99 5.   5.01 5.02 5.03\n",
      " 5.04 5.05 5.06 5.07 5.08 5.09 5.1  5.11 5.12 5.13 5.14 5.15 5.16 5.17\n",
      " 5.18 5.19 5.2  5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3  5.31\n",
      " 5.32 5.33 5.34 5.35 5.36 5.37 5.38 5.39 5.4  5.41 5.42 5.43 5.44 5.45\n",
      " 5.46 5.47 5.48 5.49 5.5  5.51 5.52 5.53 5.54 5.55 5.56 5.57 5.58 5.59\n",
      " 5.6  5.61 5.62 5.63 5.64 5.65 5.66 5.67 5.68 5.69 5.7  5.71 5.72 5.73\n",
      " 5.74 5.75 5.76 5.77 5.78 5.79 5.8  5.81 5.82 5.83 5.84 5.85 5.86 5.87\n",
      " 5.88 5.89 5.9  5.91 5.92 5.93 5.94 5.95 5.96 5.97 5.98 5.99 6.   6.01\n",
      " 6.02 6.03 6.04 6.05 6.06 6.07 6.08 6.09 6.1  6.11 6.12 6.13 6.14 6.15\n",
      " 6.16 6.17 6.18 6.19 6.2  6.21 6.22 6.23 6.24 6.25 6.26 6.27 6.28 6.29\n",
      " 6.3  6.31 6.32 6.33 6.34 6.35 6.36 6.37 6.38 6.39 6.4  6.41 6.42 6.43\n",
      " 6.44 6.45 6.46 6.47 6.48 6.49 6.5  6.51 6.52 6.53 6.54 6.55 6.56 6.57\n",
      " 6.58 6.59 6.6  6.61 6.62 6.63 6.64 6.65 6.66 6.67 6.68 6.69 6.7  6.71\n",
      " 6.72 6.73 6.74 6.75 6.76 6.77 6.78 6.79 6.8  6.81 6.82 6.83 6.84 6.85\n",
      " 6.86 6.87 6.88 6.89 6.9  6.91 6.92 6.93 6.94 6.95 6.96 6.97 6.98 6.99\n",
      " 7.   7.01 7.02 7.03 7.04 7.05 7.06 7.07 7.08 7.09 7.1  7.11 7.12 7.13\n",
      " 7.14 7.15 7.16 7.17 7.18 7.19 7.2  7.21 7.22 7.23 7.24 7.25 7.26 7.27\n",
      " 7.28 7.29 7.3  7.31 7.32 7.33 7.34 7.35 7.36 7.37 7.38 7.39 7.4  7.41\n",
      " 7.42 7.43 7.44 7.45 7.46 7.47 7.48 7.49 7.5  7.51 7.52 7.53 7.54 7.55\n",
      " 7.56 7.57 7.58 7.59 7.6  7.61 7.62 7.63 7.64 7.65 7.66 7.67 7.68 7.69\n",
      " 7.7  7.71 7.72 7.73 7.74 7.75 7.76 7.77 7.78 7.79 7.8  7.81 7.82 7.83\n",
      " 7.84 7.85 7.86 7.87 7.88 7.89 7.9  7.91 7.92 7.93 7.94 7.95 7.96 7.97\n",
      " 7.98 7.99 8.   8.01 8.02 8.03 8.04 8.05 8.06 8.07 8.08 8.09 8.1  8.11\n",
      " 8.12 8.13 8.14 8.15 8.16 8.17 8.18 8.19 8.2  8.21 8.22 8.23 8.24 8.25\n",
      " 8.26 8.27 8.28 8.29 8.3  8.31 8.32 8.33 8.34 8.35 8.36 8.37 8.38 8.39\n",
      " 8.4  8.41 8.42 8.43 8.44 8.45 8.46 8.47 8.48 8.49 8.5  8.51 8.52 8.53\n",
      " 8.54 8.55 8.56 8.57 8.58 8.59 8.6  8.61 8.62 8.63 8.64 8.65 8.66 8.67\n",
      " 8.68 8.69 8.7  8.71 8.72 8.73 8.74 8.75 8.76 8.77 8.78 8.79 8.8  8.81\n",
      " 8.82 8.83 8.84 8.85 8.86 8.87 8.88 8.89 8.9  8.91 8.92 8.93 8.94 8.95\n",
      " 8.96 8.97 8.98 8.99 9.   9.01 9.02 9.03 9.04 9.05 9.06 9.07 9.08 9.09\n",
      " 9.1  9.11 9.12 9.13 9.14 9.15 9.16 9.17 9.18 9.19 9.2  9.21 9.22 9.23\n",
      " 9.24 9.25 9.26 9.27 9.28 9.29 9.3  9.31 9.32 9.33 9.34 9.35 9.36 9.37\n",
      " 9.38 9.39 9.4  9.41 9.42 9.43 9.44 9.45 9.46 9.47 9.48 9.49 9.5  9.51\n",
      " 9.52 9.53 9.54 9.55 9.56 9.57 9.58 9.59 9.6  9.61 9.62 9.63 9.64 9.65\n",
      " 9.66 9.67 9.68 9.69 9.7  9.71 9.72 9.73 9.74 9.75 9.76 9.77 9.78 9.79\n",
      " 9.8  9.81 9.82 9.83 9.84 9.85 9.86 9.87 9.88 9.89 9.9  9.91 9.92 9.93\n",
      " 9.94 9.95 9.96 9.97 9.98 9.99]\n"
     ]
    }
   ],
   "source": [
    "a = 0.0          # Start of interval\n",
    "b = 10.0         # end of interval\n",
    "N = 1000          # number of steps. 1000 gives a nice smooth line\n",
    "h = (b-a)/N      # size of each step, i.e. delta t\n",
    "print(\"Step size h is\", h)\n",
    "x = 2          # initial condition\n",
    "\n",
    "tpoints = np.arange(a,b,h) # array of time points\n",
    "\n",
    "print(tpoints)"
   ]
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   "source": [
    "We can write a function that implements Euler's method by creating a loop over all the $t$-points. On the first iteration of the loop (i.e. $t=0$), we already have a value for $x$: the starting value. For the second iteration of the loop ($t = 0 + h$), we calculate the new value of $x$ based on the function we wrote above. This then propagates to the subsequent iterations of the loop until we have a value of $x$ for each value of $t$. We then return the entire array of xpoints."
   ]
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   "source": [
    "def Euler(x,tpoints):\n",
    "    '''Euler method function.\n",
    "    Inputs: initial x-value, array of t-values\n",
    "    Also depends on step h (global variable) and\n",
    "    requires the function f(x,t) to be defined.\n",
    "    Returns: array of propagated xpoints\n",
    "    '''\n",
    "    xpoints = []          # create an empty array of xpoints\n",
    "    \n",
    "    for t in tpoints:     # loop over all the elements of tpoints\n",
    "        xpoints.append(x) # append the current value of x to the solution array.\n",
    "        x = x + h*f(x,t)  # calculate the next value of x(look at Taylor expansion... remember to ignore h^2 and above)\n",
    "       \n",
    "    return xpoints"
   ]
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   "cell_type": "markdown",
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   "source": [
    "Now let's use this to solve the system, and plot the resulting function."
   ]
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   "execution_count": 5,
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       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xpointsEuler = Euler(x,tpoints) # calculate x(t) using Euler method\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(tpoints,xpointsEuler, label=\"Euler\")\n",
    "plt.title(\"Function evaluated using Euler's method\")\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"x(t)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maybe you can see the downside to this approach - at each stage we introduce an error due to all the terms in $h^2$ and higher that we discarded. \n",
    "\n",
    "\n",
    "One way of reducing the overall error is to make $h$ smaller, but this then means we have to do more calculations to cover the same $t$-range, and hence the calculation is slower.\n",
    "\n",
    "Another way of improving the results would be to keep the $h^2$ term in the Taylor expansion, i.e. to calculate \n",
    "$$ \\frac{1}{2} h^2 \\frac{d^2 x}{dt^2} = \\frac{1}{2} h^2 \\frac{df}{dt}, $$\n",
    "but this would only work if we have an explicit expression for $f(x,t)$ in order to calculate $\\frac{df}{dt}$, which we don't necessarily have (for example, if we have $f(x,t)$ in the form of a discrete set of experimental data points).\n",
    "\n",
    "Fortunately, there is another method that is easy to implement, and doesn't require any derivatives of $f(x,t)$ - this is the [Runge](https://en.wikipedia.org/wiki/Carl_David_Tolm%C3%A9_Runge)-[Kutta](https://en.wikipedia.org/wiki/Martin_Wilhelm_Kutta) method. Actually, it's a whole series of methods, and we'll start by looking at the simplest one, the second-order Runge-Kutta method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Second-order Runge Kutta method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the second-order Runge Kutta method, we do a Taylor expansion around $t + \\frac{1}{2}h$. Manipulation of this then leads to an expression which eliminates the terms in $h^2$, leaving an error of order ${\\rm O}(h^3)$. This derivation is included in the separate pdf appendix on Moodle for those that are interested (you don't need to understand the details of the derivation to use the method itself, but it's useful background).\n",
    "\n",
    "Here are the second-order Runge-Kutta equations,\n",
    "$$\n",
    "k_1 = hf(x,t), \\\\\n",
    "k_2 = hf(x + \\frac{1}{2}k_1, t+\\frac{1}{2}h), \\\\\n",
    "x(t+h) = x(t) + k_2,\n",
    "$$\n",
    "\n",
    "and here is the second-order Runge Kutta implemented as a function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def RungeKutta2(x,tpoints):\n",
    "    '''Second-order Runge Kutta function.\n",
    "    Inputs: initial x-value, array of t-values\n",
    "    Also depends on step h (global variable) and\n",
    "    requires the function f(x,t) to be defined.\n",
    "    Returns: array of propagated xpoints\n",
    "    '''\n",
    "    xpoints = []          # initialise empty output array\n",
    "    for t in tpoints:\n",
    "        xpoints.append(x) # append the current value of x to the solution array.\n",
    "        k1 = h * f(x,t)\n",
    "        k2 = h*f(x+0.5*k1, t+0.5*h)\n",
    "        x = x + k2        # value of x for this time point.\n",
    "    return xpoints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use this to calculate for the original function and compare the two methods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xpointsRK2 = RungeKutta2(x,tpoints)\n",
    "\n",
    "plt.figure()\n",
    "\n",
    "plt.plot(tpoints,xpointsEuler,label=\"Euler\")\n",
    "plt.plot(tpoints,xpointsRK2, \"-.\", label=\"RK2\")\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.title(\"Function evaluated using Euler and Runge Kutta methods\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"x(t)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this function we can see the results are very similar. We can still get further improvements though, by extending the Runge Kutta method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fourth-order Runge Kutta method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Taking the same approach of Taylor expanding about different points and rearranging the results to eliminate terms we can't / don't want to calculate, it's possible to come up with even more accurate (and complicated) algorithms. In general, the fourth-order Runge Kutta (i.e. the one with errors ${\\rm O}(h^5)$)is considered to have the most useful combination of simplicity and accuracy, and is the most widely used method to solve differential equations numerically.\n",
    "\n",
    "The equations are:\n",
    "$$\n",
    "k_1 = h f(x,t), \\\\\n",
    "k_2 = h f(x+\\frac{1}{2}k_1, t+\\frac{1}{2}h), \\\\\n",
    "k_3 = h f(x+\\frac{1}{2}k_2, t+\\frac{1}{2}h), \\\\\n",
    "k_4 = h f(x+k_3, t+h), \\\\\n",
    "x(t+h) = x(t) + \\frac{1}{6}(k_1 + 2k_2 + 2k_3 + k_4).\n",
    "$$\n",
    "which we implement, again as a function, in the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def RungeKutta4(x,tpoints):\n",
    "    '''Fourth-order Runge Kutta. Inputs: initial x, array of t-values\n",
    "    Also depends on step h (global variable) and\n",
    "    requires the function f(x,t) to be defined.\n",
    "    Returns: array of propagated xpoints'''\n",
    "    xpoints = [] # a new array for the fourth-order results\n",
    "    # same procedure as before. When you re-use this function, comment it appropriately!\n",
    "    for t in tpoints:\n",
    "        xpoints.append(x) \n",
    "        k1 = h*f(x,t)     \n",
    "        k2 = h*f(x+0.5*k1, t+0.5*h)\n",
    "        k3 = h*f(x+0.5*k2, t+0.5*h)\n",
    "        k4 = h*f(x+k3, t+h)\n",
    "        x = x + (k1 + 2*k2 + 2*k3 + k4)/6\n",
    "    return xpoints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can compare the results of all three methods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xpointsRK4 = RungeKutta4(x,tpoints)\n",
    "\n",
    "#print(xpointsRK4)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(tpoints,xpointsEuler)\n",
    "plt.plot(tpoints,xpointsRK2, \"-.\")\n",
    "plt.plot(tpoints,xpointsRK4, \":\")\n",
    "plt.title(\"Function evaluated using Euler and 2nd and 4th order RK\")\n",
    "plt.legend([\"Euler\", \"RK2\", \"RK4\"],loc=\"lower right\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"x(t)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, all three methods give very similar results. At this point, you may therefore be wondering what the point is of using the (slightly) more complicated 4th-order Runge Kutta method over the Euler method. To see this more clearly, let's increase the value of the step $h$ in the calculations, i.e. decrease the number of $t$-points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "h is now 1.0\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10      # number of steps. Before we used 1000\n",
    "h = (b-a)/N # size of each step (b and a defined as previously)\n",
    "print(\"h is now\", h)\n",
    "\n",
    "# set up and calculate for all three methods with N = 10\n",
    "tpointsN10 = np.arange(a,b,h) # array of time points\n",
    "xpointsEulerN10 = Euler(x,tpointsN10)\n",
    "xpointsRK2N10 = RungeKutta2(x,tpointsN10)\n",
    "xpointsRK4N10 = RungeKutta4(x,tpointsN10)\n",
    "\n",
    "# plot the results\n",
    "plt.figure()\n",
    "plt.plot(tpoints,xpointsRK4,ls=\"dashed\",lw=2,color=\"k\",label=\"RK4,1000pts\")\n",
    "plt.plot(tpointsN10,xpointsEulerN10,label=\"Euler\")\n",
    "plt.plot(tpointsN10,xpointsRK2N10,label=\"RK2\")\n",
    "plt.plot(tpointsN10,xpointsRK4N10,label=\"RK4\")\n",
    "plt.legend(loc=\"lower left\",prop={'size':10})\n",
    "plt.title(\"All methods, results for N = 10\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"x(t)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By drastically reducing the number of points to $N=10$ (and thus increasing $h$ from 0.1 to 1), we can see that none of the methods gives a good result. Clearly we've taken things too far. Let's try again with $N = 20$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "h is now 0.5\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 20      # number of steps. Before we used 1000\n",
    "h = (b-a)/N # size of each step (b and a defined as previously)\n",
    "print(\"h is now\", h)\n",
    "\n",
    "\n",
    "# set up and calculate fn using all 3 methods with N = 20\n",
    "tpointsN20 = np.arange(a,b,h) # array of time points\n",
    "xpointsEulerN20 = Euler(x,tpointsN20)\n",
    "xpointsRK2N20 = RungeKutta2(x,tpointsN20)\n",
    "xpointsRK4N20 = RungeKutta4(x,tpointsN20)\n",
    "\n",
    "# plot the results\n",
    "plt.figure()\n",
    "plt.plot(tpoints,xpointsRK4,ls=\"dashed\",lw=2,color=\"k\",label=\"RK4,1000pts\")\n",
    "plt.plot(tpointsN20,xpointsEulerN20,label=\"Euler\")\n",
    "plt.plot(tpointsN20,xpointsRK2N20,label=\"RK2\")\n",
    "plt.plot(tpointsN20,xpointsRK4N20,label=\"RK4\")\n",
    "plt.legend(loc=\"lower left\",prop={'size':10})\n",
    "plt.title(\"All three methods, results for N = 20\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"x(t)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can see clearly that the 4th-order Runge Kutta outperforms the other methods, even with relatively few points. As a final demonstration, we'll use $N=30$ to show that there is remarkably little difference from the $N=1000$ results for the 4th-order Runge Kutta (we won't actually quantify this difference here though)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "h is now 0.3333333333333333\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 30      # number of steps. Before we used 1000\n",
    "h = (b-a)/N # size of each step (b and a defined as previously)\n",
    "print(\"h is now\", h)\n",
    "\n",
    "# set up and calculate for all three methods with N = 30\n",
    "tpointsN30 = np.arange(a,b,h) # array of time points\n",
    "xpointsEulerN30 = Euler(x,tpointsN30)\n",
    "xpointsRK2N30 = RungeKutta2(x,tpointsN30)\n",
    "xpointsRK4N30 = RungeKutta4(x,tpointsN30)\n",
    "\n",
    "# plot results\n",
    "plt.figure()\n",
    "plt.plot(tpoints,xpointsRK4,ls=\"dashed\",lw=2,color=\"k\",label=\"RK4,1000pts\")\n",
    "plt.plot(tpointsN30,xpointsEulerN30,label=\"Euler\")\n",
    "plt.plot(tpointsN30,xpointsRK2N30,label=\"RK2\")\n",
    "plt.plot(tpointsN30,xpointsRK4N30,label=\"RK4\")\n",
    "plt.legend(loc=\"lower left\",prop={'size':10})\n",
    "plt.title(\"Results for N = 30\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"x(t)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-success\">\n",
    "<h2>What to do now</h2>\n",
    "\n",
    "<ol>\n",
    "<li>Go back to the cell near the top of the notebook where we defined f(x,t). Change the function (best to comment out the original code rather than deleting it) to instead calculate for an exponential decay $-2e^{-t}$ and set the initial value of $x$ to 2.0. Rerun the whole notebook (HINT: use the \"Run All\" command from the cell menu). What do you notice now about the Euler method?</li>\n",
    "\n",
    "<li>Try with some other first-order differential equations!</li>\n",
    "</ol>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The 4th order Runge-Kutta method is still the best method since it outperforms outher method with lower h. As the h decreases, the Euler method becomes drastically better while the other methods become only a little better. However, the Euler methods seems to be drastically less accurate than the other methods. Furthermore, in the first three graphs, the Euler method is a little (vertically) lower."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Your task: Solving for a low-pass filter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <div class=\"alert alert-success\"> For this task, start a new notebook from scratch. <br> <br> Remember to use text cells to describe your reasoning and results, and comments to annotate the code. <br> <br>You can cut and paste code, equations and images from this notebook if you want,  as long as your notebook makes it clear where you have pasted material and where it came from. </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This image shows an electronic circuit for a low-pass filter (if you can't see the image below, follow [this link](http://commons.wikimedia.org/wiki/File:1st_Order_Lowpass_Filter_RC.svg)).  The purpose of such a filter is to cut off the high-frequency parts of the input signal (i.e. it lets the *low* frequency parts of the signal *pass*). \n",
    "\n",
    "![circuit diagram](http://upload.wikimedia.org/wikipedia/commons/thumb/e/e0/1st_Order_Lowpass_Filter_RC.svg/500px-1st_Order_Lowpass_Filter_RC.svg.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $I$ be the current that flows through the resistor $R$ and into the capacitor $C$, with a charge $Q$ on the capacitor. Then we have\n",
    "\n",
    "$$\n",
    "IR = V_{\\rm in} - V_{\\rm out}, \\\\\n",
    " Q = C V_{\\rm out}, \\\\\n",
    " I = \\frac{dQ}{dt}.$$\n",
    "\n",
    "Rearranging this gives us a first-order differential equation:\n",
    "$$ \\frac{dV_{\\rm out}}{dt} = \\frac{1}{RC} ( V_{\\rm in} - V_{\\rm out}). $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Let the input signal $V_\\text{in}$ be a square wave (in Volts) defined as: \n",
    "$$ V_{\\rm in} = \\begin{cases} 1 & \\text{if } \\lfloor 2t \\rfloor\\  \\text{is even}, \\\\ \n",
    "-1  & \\text{if } \\lfloor 2t \\rfloor\\  \\text{is odd}, \\end{cases} \n",
    "$$\n",
    "where the notation $\\lfloor x \\rfloor$ means $x$ rounded *down* to the next lowest integer, and $t$ is in units of microseconds ($\\mu$s). Write a Python function to represent this mathematical function. \n",
    "     * *Hint 1: you may find the function [np.floor](http://docs.scipy.org/doc/numpy/reference/generated/numpy.floor.html) useful here.*\n",
    "     * *Hint 2: A good way of determining whether an integer $n$ is odd or even is to use a construct like $(-1)^n$*\n",
    "2. Check your function is working correctly by plotting it in the range $0 \\leq t \\leq 10 \\mu$s. Make sure you include enough time points to ensure the signal is properly square.\n",
    "2. Solve this using the fourth-order Runge-Kutta method by following the basic procedure we've used in this notebook, i.e.:\n",
    "     * Write a function to represent the RHS of the differential equation (which will use the function for $V_{\\rm in}$)\n",
    "     * Either use the fourth-order Runge-Kutta function from this notebook (copy and paste, and add your own comments) or rewrite your own version.\n",
    "     * Define the start and end points, initial conditions, create an array of time values and solve.\n",
    "3. Plot the input square wave and the output of this (on the same plot) for the range $0\\leq t \\leq 10$ $\\mu$s when the time constant $RC = 1 \\mu$s. Repeat this for time constants $RC= 0.1$ and $0.01 \\mu$s (i.e. three plots, each with an input and output line). Use the initial condition $V_\\text{out} = 0 {\\textrm V}$.\n",
    "4. In a text cell, describe what you see and what you think the circuit is doing. *(Hint: Why do you think it is called a \"low-pass filter\"?)*\n",
    "5. Now change the form of $V_\\rm{in}$ from a square wave to a sine wave: $V_{\\rm in} = \\sin(2t)$. What effect does the filter have now?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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