{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Initial Value Problems for ODEs, Part 2: Runge-Kutta Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Updated (slightly) on Monday March 29.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- Section 6.4 *Runge-Kutta Methods and Applications* of [Sauer](../references.html#Sauer);\n",
    "in particular Sub-section 6.4.1.\n",
    "- Section 5.4 *Runge-Kutta Methods* of [Burden&Faires](../references.html#Burden-Faires)\n",
    "- Sections 7.1 and 7.2 of [Chenney&Kincaid](../references.html#Chenney-Kincaid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "# Shortcuts for some favorite commands:\n",
    "from numpy import linspace\n",
    "from matplotlib.pyplot import figure, plot, grid, title, xlabel, ylabel, legend"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Introduction\n",
    "------------\n",
    "\n",
    "The original Runge-Kutta method is the fourth order accurate one to be described below, which is still used a lot, though with some modifications.\n",
    "\n",
    "However, the name is now applied to a variety of methods based on a similar strategy, so first, here are a few simpler methods, all of some value, at least for small, low precision calculations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Euler's Method as a Runge-Kutta method\n",
    "\n",
    "The simplest of all methods of this general form is Euler's method.\n",
    "To set up the notation to be used below, rephrase it this way:\n",
    "\n",
    "To get from $(t, u)$ to an approximation of $(t+h, u(t+h))$, use the approximation\n",
    "\n",
    "$$\\begin{split}\n",
    "K_1 &= h f(t, u)\n",
    "\\\\\n",
    "u(t+h) &\\approx u + K_1\n",
    "\\end{split}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Second order Runge-Kutta methods\n",
    "\n",
    "We have seen that the global error of Euler's method is $O(h)$: it is only first order accurate.\n",
    "This is often insufficient, so it is more common even for small, low precision calculation to use one of several second order methods:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Explicit Trapezoid Method (a.k.a. the Improved Euler method or Huen's method)\n",
    "\n",
    "One could try to adapt the trapezoid method for integrating $f(t)$ to solve $du/dt = f(t)$\n",
    "\n",
    "$$\n",
    "u(t + h) = u(t) + \\int_{t}^{t + h} f(s) ds \\approx u(t) + h \\frac{f(t) + f(t+h)}{2}\n",
    "$$\n",
    "\n",
    "to solving the ODE $du/dt = f(t, u)$ but there is a problem that needs to be overcome:\n",
    "\n",
    "we get\n",
    "\n",
    "$$\n",
    "u(t + h) \\approx u(t) + h \\frac{f(t, u(t)) + h f(t+h, u(t+h))}{2}\n",
    "$$\n",
    "\n",
    "and inserting the values $U_i \\approx u(t_i)$ and so on gives\n",
    "\n",
    "$$\n",
    "U_{i+1} \\approx U_i + h \\frac{f(t_i, U_i) + f(t_{i+1}, U_{i+1}))}{2}\n",
    "$$\n",
    "\n",
    "This is known as the **Implicit Trapezoid Rule**, because the value $U_{i+1}$ that we seek appears at the right-hand side too: we only have an *implicit* formula for it.\n",
    "\n",
    "On one hand, one can in fact use this formula, by solving the equation at each time step for the unknown $U_{i+1}$;\n",
    "for example, one can use methods seen in earlier sections such as fixed point iteration or the secant method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will return to this in a later section;\n",
    "however, for now we get around this more simply by inserting an approximation at right — the only one we know so far, given by Euler's Method.\n",
    "That is:\n",
    "\n",
    "- replace $u(t+h)$ at right by the tangent line approximation $u(t+h) \\approx u(t) + hf(t, u(t))$, giving\n",
    "\n",
    "$$\n",
    "u(t + h) \\approx u(t) + h \\frac{f(t, u(t)) + f(t+h, u(t) + hf(t, u(t)))}{2}\n",
    "$$\n",
    "\n",
    "and for the formulas in terms of the $U_i$, replace $U_{i+1}$ at right by $U_{i+1} \\approx U_i + h f(t_i, U_i)$, giving\n",
    "\n",
    "$$\n",
    "U_{i+1} = U_i + h \\frac{f(t_i, U_i) + f(t_{i+1}, U_i + h f(t_i, U_i))}{2}\n",
    "$$\n",
    "\n",
    "This is the **Explicit Trapezoid Rule**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is convenient to break this down into two stages, one for each evaluation of $f(t, u)$:\n",
    "\n",
    "$$\\begin{split}\n",
    "K_1 &= h f(t, u)\n",
    "\\\\\n",
    "K_2 &= h f(t+h, u + K_1)\n",
    "\\\\\n",
    "u(t+h) &\\approx u + \\frac{1}{2}(K_1 + K_2)\n",
    "\\end{split}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For equal sized time steps, this leads to the algorithm\n",
    "\n",
    "$$\\begin{split}\n",
    "U_0 &= u_0\n",
    "\\\\\n",
    "U_{i+1} &= U_i + \\frac{1}{2}(K_1 + K_2),\n",
    "\\\\\n",
    "&\\quad \\text{where}\n",
    "\\\\\n",
    "K_1 &= h f(t_i, U_i)\n",
    "\\\\\n",
    "K_2 &= h f(t_{i+1}, U_i + K_1)\n",
    "\\end{split}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will see that, despite the mere first order accuracy of the Euler approximation used in getting $K_2$, this method is second order accurate; the key is the fact that any error in the approximation used for $f(t+h, u(t+h))$ gets multiplied by $h$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1\n",
    "\n",
    "A) Verify that for the simple case where $f(t, u) = f(t)$,\n",
    "this gives the same result as the composite trapezoid rule for integration.\n",
    "\n",
    "B) Do one step of this method for the canonical example $du/dt = ku$, $u(t_0) = u_0$.\n",
    "It will have the form $U_1 = G U_0$ where the growth factor $G$ approximates the factor $g=e^{kh}$ for the exact solution $u(t_1) = g u(t_0)$ of the ODE.\n",
    "\n",
    "C) Compare to $G=1+kh$ seen for Euler's method.\n",
    "\n",
    "D) Use the previous result to express $U_i$ in terms of $U_0=u_0$, as done for Euler's method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def explicitTrapezoid(f, a, b, u_0, n=100, demoMode=False):\n",
    "    \"\"\"Use the Explict Trapezoid Method (a.k.a Improved Euler)\n",
    "    to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "    u = np.empty_like(t)\n",
    "    u[0] = u_0\n",
    "    for i in range(n):\n",
    "        K_1 = f(t[i], u[i])*h\n",
    "        K_2 = f(t[i]+h, u[i]+K_1)*h\n",
    "        u[i+1] = u[i] + (K_1 + K_2)/2.\n",
    "    return (t, u)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As always, this function can now also be imported from `numerical_methods_module`, with\n",
    "\n",
    "    from numerical_methods_module import explicitTrapezoid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Examples\n",
    "\n",
    "For all methods in this section, we will solve for versions of Example 2 and 4 in the section\n",
    "[Solving Initial Value Problems for Ordinary Differential Equations, Part 1](ODE-IVP-1-basics-and-Euler-python.ipynb).\n",
    "\n",
    "$$\n",
    "\\frac{du}{dt} = f_1(t, u) = K u\n",
    "$$\n",
    "\n",
    "with general solution\n",
    "\n",
    "$$\n",
    "u(t) = u_1(t; a, u_0) = u_0 e^{t-a}\n",
    "$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\n",
    "\\frac{du}{dt}  = K(\\cos(t) - u) - \\sin(t)\n",
    "$$\n",
    "\n",
    "with general solution\n",
    "\n",
    "$$\n",
    "u(t) = u_2(t; a, u_0) = \\cos(t) + C e^{-K t},\\quad C = (u_0 - \\cos(a)) e^{K a}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For comparison to Euler's Method, the same examples are done with it [below](#euler-redux)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_1(t, u):\n",
    "    \"\"\"The simplest \"genuine\" ODE, (not just integration)\n",
    "    The solution is u(t) = u(t; a, u_0) = u_0 exp(t-a)\n",
    "    \"\"\"\n",
    "    return K*u\n",
    "def u_1(t): return u_0 * np.exp(K*(t-a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_2(t, u):\n",
    "    \"\"\"A simple more \"generic\" test case, with f(t, u) depending on both variables.\n",
    "    The solution for a=0 is u(t) = u(t; 0, u_0) = cos t + (u_0 - 1) e^(-Kt)\n",
    "    The solution in general is u(t) = u(t; a, u_0) = cos t + C e^(-K t), C = (u_0 - cos(a)) exp(K a)\n",
    "    \"\"\"\n",
    "    return  K*(np.cos(t) - u) - np.sin(t)\n",
    "def u_2(t): return np.cos(t) + C * np.exp(-K*t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "    a = 1.\n",
    "    b = 3.\n",
    "    u_0 = 2.\n",
    "    K = 1.\n",
    "    n = 10\n",
    "\n",
    "    (t, U) = explicitTrapezoid(f_1, a, b, u_0, n, demoMode=True)\n",
    "    h = (b-a)/n\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Solving du/dt = Ku, {a=}, {u_0=}  by the Explicit Trapezoid Method\")\n",
    "    plt.plot(t, u_1(t), 'g', label=\"Exact solution\")\n",
    "    plt.plot(t, U, 'b:', label=f\"Solution with h={h:0.3}\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Error\")\n",
    "    plt.plot(t, U - u_1(t))\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it.\n",
    "    \n",
    "    def f_2(t, u):\n",
    "        \"\"\"A simple more \"generic\" test case, with f(t, u) depending on both variables.\n",
    "        The solution for a=0 is u(t) = u(t; 0, u_0) = cos t + (u_0 - 1) e^(-Kt)\n",
    "        The solution in general is u(t) = u(t; a, u_0) = cos t + C e^(-K t), C = (u_0 - cos(a)) exp(K a)\n",
    "        \"\"\"\n",
    "        return  K*(np.cos(t) - u) - np.sin(t)\n",
    "    def u_2(t): return np.cos(t) + C * np.exp(-K*t)\n",
    "\n",
    "    a = 1.\n",
    "    b = a + 4 * np.pi  # Two periods\n",
    "    u_0 = 2.\n",
    "    K = 2.\n",
    "    n = 50\n",
    "\n",
    "    (t, U) = explicitTrapezoid(f_2, a, b, u_0, n)\n",
    "    C = (u_0 - np.cos(a)) * np.exp(K*a)\n",
    "    h = (b-a)/n\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Solving du/dt = K(cos(t) - u) - sin(t), {K=}, {a=}, {u_0=} by the Explicit Trapezoid Method\")\n",
    "    plt.plot(t, u_2(t), 'g', label=\"Exact solution\")\n",
    "    plt.plot(t, U, 'b:', label=f\"Solution with h={h:0.3}\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    \n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Error\")\n",
    "    plt.plot(t, U - u_2(t))\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Explicit Midpoint Method (a.k.a. Modified Euler)\n",
    "\n",
    "If we start with the Midpoint Rule for integration in place of the Trapezoid Rule, we similarly get an approximation\n",
    "\n",
    "$$\n",
    "u(t + h) \\approx u(t) + h f(t + h/2, u(t + h/2))\n",
    "$$\n",
    "\n",
    "This has the slight extra complication that it involves three values of $u$ including $u(t+h/2)$ which we are not trying to evaluate.  We deal with that by making yet another approximation, using an average of $u$ values:\n",
    "\n",
    "$$\n",
    "u(t+h/2) \\approx \\frac{u(t) + u(t+h)}{2}\n",
    "$$\n",
    "\n",
    "leading to\n",
    "\n",
    "$$\n",
    "u(t + h) \\approx u(t) + h f\\left( t + h/2, \\frac{u(t) + u(t+h)}{2} \\right)\n",
    "$$\n",
    "\n",
    "and in terms of $U_i \\approx u(t_i)$, the **Implicit Midpoint Rule**\n",
    "\n",
    "$$\n",
    "U_{i+1} = U_i + h f\\left( t + h/2, \\frac{U_i + U_{i+1}}{2} \\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will see late that this is a particularly useful method in some situations, such as long-time solutions of ODEs that describe the motion of physical systems with conservation of momentum, angular momentum and kinetic energy. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, for now we again seek a more straightforward *explicit* method; using the same tangent line approximation strategy as above gives the **Explicit Midpoint Rule**\n",
    "\n",
    "$$\\begin{split}\n",
    "K_1 &= h f(t, u)\n",
    "\\\\\n",
    "K_2 &= h f(t+h/2, u + K_1/2)\n",
    "\\\\\n",
    "u(t+h) &\\approx u + K_2\n",
    "\\end{split}$$\n",
    "\n",
    "and thus for equal-sized time steps, the algorithm\n",
    "\n",
    "$$\\begin{split}\n",
    "U_0 &= u_0\n",
    "\\\\\n",
    "U_{i+1} &= U_i + K_2\n",
    "\\\\\n",
    "&\\quad \\text{where}\n",
    "\\\\\n",
    "K_1 &= h f(t_i, U_i)\n",
    "\\\\\n",
    "K_2 &= h f(t_{i}+h/2, U_i + K_1/2)\n",
    "\\end{split}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 2 (a lot like Exercise 1)\n",
    "\n",
    "A) Verify that for the simple case where $f(t, u) = f(t)$,\n",
    "this give the same result as the composite midpoint rule for integration (same comment as above).\n",
    "\n",
    "B) Do one step of this method for the canonical example $du/dt = ku$, $u(t_0) = u_0$.\n",
    "It will have the form $U_1 = G U_0$ where the growth factor $G$ approximates the factor $g=e^{kh}$ for the exact solution $u(t_1) = g u(t_0)$ of the ODE.\n",
    "\n",
    "C) Compare to the growth factors $G$ seen for previous methods, and to the growth factor $g$ for the exact solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3\n",
    "\n",
    "A) Apply Richardson extrapolation to one step of Euler's method, using the values given by step sizes $h$ and $h/2$.\n",
    "\n",
    "B) This should give a second order accurate method, so compare it to the above two methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def explicitMidpoint(f, a, b, u_0, n=100, demoMode=False):\n",
    "    \"\"\"Use the Explicit Midpoint Method (a.k.a Modified Euler)\n",
    "    to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "    u = np.empty_like(t)\n",
    "    u[0] = u_0\n",
    "    for i in range(n):\n",
    "        K_1 = f(t[i], u[i])*h\n",
    "        K_2 = f(t[i]+h/2, u[i]+K_1/2)*h\n",
    "        u[i+1] = u[i] + K_2\n",
    "    return (t, u)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, available for import with\n",
    "\n",
    "    from numerical_methods_module import explicitMidpoint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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p8brSoojIaVKIFhFpRaLCPZyXlcx5WceOVu8uPsyyHUW8sehzNheU8MH6vQAkx0YwKjulLlR3S43FTKFaRKQxFKJFRFoxM6NzUgydk2JIKN5ETk4Ou4sPs3hLIblb9rN4SyFvr9kDQId2UYz2X5lxdI9UOiVGB7l6EZHQpRAtItLGdEqM5uqhnbl6aGecc2wvLCd3y35ytxSyYOO+ulPrdU2J8YfqVEZlp9A+Xl9UFBE5qkkh2sySgVeBLGA7cI1zrqiBcROB3wEe4Hnn3MP+9d8C/gvoCwx3zi1tSj0iIhIYM6NbaizdUmO5YURXamsdGwtKyN1cSO6WQt5atYdXluwEoFd6HKO7pzKqewoju6WQEBMe5OpFRIKnqUeiHwDmOuceNrMH/Ms/rT/AzDzAU8DFwC7gMzOb5ZxbB3wOXAX8oYl1iIjIGRAWZvTp0I4+Hdrx3fO7UV1Ty9r8Q+T6p3/M+CyPF3O3Ywb9MxLqpn+cl5VMbKT+uCkibUdT93hXAjn++9OB+ZwQooHhwGbn3FYAM5vhf9w659x6/7omliEiImeD1xPGwC6JDOySyF053amsrmXlzuK66R8vfLyNPyzcijfMGNQlsW76x+DMRKLCPcEuX0TkrGlqiE53zu0BcM7tMbO0BsZ0AnbWW94FjGji64qISBBEeMPqzlV97wTfBWCW7jjgP1JdyJMfbuaJeZuJ9IYxLCuJ0d1TGdMjlQGdEnQ6PRFpVcy5rz/5vpl9AHRoYNODwHTnXGK9sUXOuaQTHv8t4BLn3G3+5RvxzX++p96Y+cBPvm5OtJlNBaYCpKenD50xY8bXv7OzoLS0lLi4uGZ/3ZZK/QqcehYY9SswzdGv8irHF0U1rC+sYf2BWnaW1ALQLgIGtvcyKM3DOSkeoryhH6j1+QqM+hUY9SswwezXuHHjljnnhp24/pRHop1zE062zcz2mllH/1HojkBBA8N2AV3qLXcG8htR84l1TAOmAQwbNszl5OQE+hRNNn/+fILxui2V+hU49Sww6ldgmqtfl9a7X1hawaLN+/lgfQHzvyjgo90VRHjCGNk9hfF90rioTxpdkmPOek2nQ5+vwKhfgVG/AhOK/WrqdI5ZwM3Aw/7bNxsY8xnQ08y6AbuBa4Hrm/i6IiLSAqTERXLloE5cOagTVTW1LN1exLwNe5m7voCHZq3loVlr6Z0ez0V905jQN41BXZLwaNqHiLQATQ3RDwOvmdmtQB7wLQAzy8B3KrtLnXPVZnY38C6+U9y94Jxb6x/3TeD3QHvgbTNb6Zy7pIk1iYhICAr3hDHKfzaPBy/rx9Z9pczbUMDc9QU8t3Arz8zfQnJsBDm92zO+Tzpje6USH6XT6IlIaGpSiHbOFQLjG1ifT72/6Dnn5gBzGhj3BvBGU2oQEZGWKbt9HNnt47jtgmwOHq5i4cZ9zNtQwLwNBcxcvptwjzG8WzLj+6Qzvm8aXVNig12yiEgdndRTRESCLiE6nMkDM5g8MIPqmlpW7Czmg/V7mbe+gF++tY5fvrWOHmlxjO+Txvi+6QzJTMTrCQt22SLShilEi4hISPF6wjgvK5nzspL52aS+5BWWM3fDXuZtKKg7L3ViTDg5vdpzUd90LuzVnoRoTfsQkealEC0iIiEtMyWGW8Z045Yx3Sg5UsWiTb6zfXz4RQH/WJmPJ8w4LyuJCX3TuahPGtntddowETn7FKJFRKTFiI8KZ9K5HZl0bkdqah0rdxbXne3j12+v59dvryc7NZaL+qRxUd80hmcla9qHiJwVCtEiItIiecKMoV2TGNo1ifsu6cOuovK6s328tHgHzy/aRmpcBJee25ErBmYwJDNJV00UkTNGIVpERFqFzkkx3DQqi5tGZVFWUc1Hm/Yxe9UeXv1sJy8t3kFGQhSXD8zgioEZnJPRDjMFahE5fQrRIiLS6sRGepnYvyMT+3ektKKaD9btZfaqfP708TamLdxKdmqsP1B3pEdafLDLFZEWSCFaRERatbhIL1MGd2LK4E4Ul1fyzudfMnt1Pk/O28QTczfRt2M7Jg/syOQBGSF7CXIRCT0K0SIi0mYkxkRw7fBMrh2eSUHJEeas3sOsVfn85p0v+M07XzA4M5HJAzK4fEDHYJcqIiFOIVpERNqktPgovjOmG98Z042dB8p5a/UeZq/K55dvreNXb6+jT1IY+dF5TOrfgaTYiGCXKyIhRiFaRETavC7JMdyV0527crqzuaCU2avyeXXxZn7+xhr+883PuaBnKlcMyuDifh2Ii9SvThFRiBYRETlOj7Q4fnhxLwZ5d9O+1xBmr87nrVV7+OGrq4j0rmF83zQmD8hgXJ80osI9wS5XRIJEIVpERKQBZkb/Tgn075TATy/pw4qdRcxamc/ba/YwZ82XxEV6+Ua/dCYPzOD8nqmE66IuIm2KQrSIiMgphIUZQ7smM7RrMv9xeT8+3XaAWSvz+efne5i5YjeJMeFM6u+7qMvwbsl4dFEXkVZPIVpERCQAXk8YY3qkMqZHKr+a0p+FG/cxe3U+b67czStL8kiLj+SKgRlcOzyTHmlxwS5XRM4ShWgREZHTFOENY0K/dCb0S6e8spp5GwqYtTKfF3O38/yibQzvlsz1wzOZ2L+D5k+LtDIK0SIiImdATISXywdkcPmADPaVVPD6sl3M+CyPe19dSeLscK4a3JnrhnehZ7qukCjSGihEi4iInGHt4yO5K6c7d4zNZvHWQv66JI8/f7KdFz7exnlZSVw3PJNLz+2oo9MiLZhCtIiIyFkSFmZ186f3l1bw92W7eGVJHj96bRW/mL2Oq4Z04rrhmfTS0WmRFkchWkREpBmkxkVyx4Xdmeo/Ov3Kkp28/MkO/vTxdoZ19R2dvmyAjk6LtBQK0SIiIs3IzBjdPZXR3VMpLO3HzOW+s3r8+G+r+MXstVw1pDPXDc+kdwcdnRYJZQrRIiIiQZISF8ntY7O57YJufLrtAK8syeOvn+bxYu52hmQmct3wTC4fkEF0hI5Oi4QahWgREZEgMzNGZqcwMjuFhyZXMnP5Lv66JI/7Xl/NL99axzcH++ZO9+3YLtilioifQrSIiEgISY6N4LYLsrn1/G4s8R+dnvHZTl5avINBXRK5fngmlw/sSEyEfoWLBJP+DxQREQlBZsaI7BRGZKfwUFklM1f45k7f//fV/OqtdVw5OIPrhmdyTkZCsEsVaZMUokVEREJcUmwEt57fje+OyWLpjiJe+TSP15bu4uVP8hjYOYHrR/jmTsdG6te6SHMJC3YBIiIi0jhmxnlZyTz27UEs+fl4Hprcj/LKGn769zWM+O+5PPjGGjYXlAa7TJE2Qf9kFRERaYESYyK4ZUw3vjM6i+V5Rfz10528vmwXf/k0jwl907nzwmyGZSUHu0yRVkshWkREpAUzM4Z2TWZo12R+fmkfpi/ewUuLt3P1s3sZ2jWJqWOzubhvOmFhFuxSRVoVTecQERFpJVLiIvnRxb3IfeAifnHFOew9dIQ7/ryMCb9dwCtL8jhSVRPsEkVaDYVoERGRViYmwsvNo7OY/5Mcfn/dYGIiPPxs5hrO/98PeerDzRwsrwp2iSItnqZziIiItFJeTxiTB2Zw+YCOLN5SyLMLt/LIu1/w1IebuW54Jt89vxudEqODXaZIi6QQLSIi0sqZGaN7pDK6Ryrr8g/x3EdbeTF3O9NztzN5YAZTx2braogiAdJ0DhERkTakX0Y7fvvtQSy8fxw3j87i3bVfMul3H3HTC0vI3bwf51ywSxRpERSiRURE2qBOidH8x+X9WPzAeO67pDfr8g9x/fOfcsWTHzN7VT7VNbXBLlEkpDUpRJtZspm9b2ab/LdJJxk30cy+MLPNZvZAvfWPmNkGM1ttZm+YWWJT6hEREZHAJMSE8/1xPVj003H8z1XnUlZRzT2vrGDco/OZnrud8srqYJcoEpKaeiT6AWCuc64nMNe/fBwz8wBPAZOAfsB1ZtbPv/l9oL9zbgCwEfhZE+sRERGR0xAV7uG64Zl88KML+cONQ2kfF8lDs9Yy5uF5/Pb9jRSWVgS7RJGQ0tQQfSUw3X9/OjClgTHDgc3Oua3OuUpghv9xOOfec84d/SfuJ0DnJtYjIiIiTRAWZlxyTgdmfm8Mr985iqFdk/nd3E2Mfnge//GPz9lRWBbsEkVCgjXlCwRmVuycS6y3XOScSzphzNXAROfcbf7lG4ERzrm7Txg3G3jVOffySV5rKjAVID09feiMGTNOu+7TVVpaSlxcXLO/bkulfgVOPQuM+hUY9Ssw6tcx+aW1vLO9itzd1dQ4GNbBw6Ru4WQneOrGqF+BUb8CE8x+jRs3bplzbtiJ6095ijsz+wDo0MCmBxv52g1dZ/S45G5mDwLVwF9O9iTOuWnANIBhw4a5nJycRr78mTN//nyC8botlfoVOPUsMOpXYNSvwKhfx7seKDh0hD/lbuflT3bw2eIjjMxO5o4Lu5PTqz0LFixQvwKgz1dgQrFfpwzRzrkJJ9tmZnvNrKNzbo+ZdQQKGhi2C+hSb7kzkF/vOW4GLgfGO51XR0REJGSltYvipxP78P1xPZixJI8/LtrGLX/6jN7p8YxLr2ZsrSMsrKFjZyKtT1PnRM8Cbvbfvxl4s4ExnwE9zaybmUUA1/ofh5lNBH4KXOGcK29iLSIiItIM4iK93HZBNgvuG8dj1wwE4NnVFVz6xEfM27BX55qWNqGpIfph4GIz2wRc7F/GzDLMbA6A/4uDdwPvAuuB15xza/2PfxKIB943s5Vm9mwT6xEREZFmEuEN46ohnfnnDy7gzgGRHK6q4bsvLuVbzy5mybYDwS5P5Kxq0mW/nXOFwPgG1ucDl9ZbngPMaWBcj6a8voiIiARfWJgxMsPLj789lteW7uR3H2zimj8sJqd3e+67pDfnZCQEu0SRM05XLBQREZEzItwTxg0jurLgvnE8MKkPK/KKueyJRdzzygq27dep8aR1UYgWERGRMyo6wsOdF3Zn4f3juHtcDz5Yt5cJjy3gZzPX8OXBI8EuT+SMUIgWERGRsyIhOpyfXNKbBffn8K8jMnl92U4ufORD/mfOeorKKoNdnkiTKESLiIjIWZUWH8UvruzPvB/ncNmAjkz7aCtjf/Mhv5+7ibKK6lM/gUgIUogWERGRZtElOYbHrhnEOz8Yy8juKTz6/kYufORDXvx4GxXVNcEuTyQgCtEiIiLSrHp3iOe5m4Yx83uj6ZEWx3/NXsdF/7eA15ftoqZW55iWlkEhWkRERIJiSGYSr9w+kpe+O5zk2Ah+8rdVTHx8Ie98/qUu2CIhTyFaREREgsbMGNurPbPuHsPTNwyhxjnufHkZU57OJXfz/mCXJ3JSCtEiIiISdGbGped25L17x/K//3IuBYeOcP3zn/Kvz3/Kqp3FwS5P5CsUokVERCRkeD1hfPu8TD78SQ7/fllf1uYf5MqnPuaul5exuaA02OWJ1FGIFhERkZATFe7htguyWXj/OH4wvicLN+7jG79dwH1/W8Xu4sPBLk9EIVpERERCV3xUOD+8uBcL7x/HLWO68ebKfMY9Mp9fzl5HYWlFsMuTNkwhWkREREJeSlwk/3F5Pz68L4cpgzN4MXcbY3/zIb99fyOHK3WOaWl+CtEiIiLSYnRKjOY3Vw/kvR9eyIW92/O7uZuY8NgC3lur0+JJ81KIFhERkRanR1ocT98wlFenjiQ20sPUPy/j1ulLySssD3Zp0kYoRIuIiEiLNSI7hbf/7QJ+fmkfPtlayMW/XcATczfpMuJy1ilEi4iISIsW7glj6tjuzP3xhUzom85j729k4uMfsXDjvmCXJq2YQrSIiIi0Ch0TonnqhiG89N3hANz0whK+95dl7DmoU+LJmacQLSIiIq3K2F7teefeC/jxxb2Yu76A8Y8uYNrCLVTV1Aa7NGlFFKJFRESk1Yn0erhnfE8++NGFjMpO4b/nbOCyJz7i062FwS5NWgmFaBEREWm1uiTH8MfvnMdzNw2jrKKGb0/7hB+9upJ9JbpQizSNQrSIiIi0ehf3S+eDH13I98d1Z/bqfC56dD7Tc7dTU6tzS8vpUYgWERGRNiE6wsN9l/ThnXvHMrBzIg/NWsuVTy1iRV5RsEuTFkghWkRERNqU7u3j+POtw/n9dYPZV1LBVc/k8rOZqykqqwx2adKCKESLiIhIm2NmTB6Ywdwf53DrmG68tnQXFz06n1c/y6NWUzykERSiRUREpM2Ki/Ty75f34+1/O58eaXH89O9ruPrZXNbmHwx2aRLiFKJFRESkzevToR2v3TGK//vWQHYUljP594v4r1lrOXSkKtilSYhSiBYRERHBN8Xj6qGdmffjHK4fkcn0xdsZ/+gC3ly5G+c0xUOOpxAtIiIiUk9CTDi/nnIub35/DB0TovjBjJVc/9ynbC4oCXZpEkIUokVEREQaMKBzIm98bwy/ntKftfkHmfj4Rzz8zw2UV1YHuzQJAQrRIiIiIifhCTP+dWRX5v0khymDO/Hsgi1MeHQB73y+R1M82jiFaBEREZFTSI2L5P++NZC/3TmKdtHh3Pnycu748zIKS3X58LZKIVpERESkkc7LSuate87nZ5P6MP+LfVzy+ELmrt8b7LIkCBSiRURERALg9YRxx4XdmXXPGFLjIrl1+lJ+NnMNZRWaK92WNClEm1mymb1vZpv8t0knGTfRzL4ws81m9kC99b8ys9VmttLM3jOzjKbUIyIiItJc+nRox5t3j+GOC7OZ8Vkelz7xEct2FAW7LGkmTT0S/QAw1znXE5jrXz6OmXmAp4BJQD/gOjPr59/8iHNugHNuEPAW8J9NrEdERESk2UR6PfxsUl9m3D6S6hrHt57N5dH3vqCqpjbYpclZ1tQQfSUw3X9/OjClgTHDgc3Oua3OuUpghv9xOOcO1RsXC+hrriIiItLijMhO4Z17L+Cbgzvz+3mbuerpXDYXlAa7LDmLrCmnZzGzYudcYr3lIudc0gljrgYmOudu8y/fCIxwzt3tX/5/wE3AQWCcc27fSV5rKjAVID09feiMGTNOu+7TVVpaSlxcXLO/bkulfgVOPQuM+hUY9Ssw6ldg1K9jPvuymulrK6iogW/3juCiTC9hZseNUb8CE8x+jRs3bplzbtiJ672neqCZfQB0aGDTg418bWtgXV1yd849CDxoZj8D7gYeauhJnHPTgGkAw4YNczk5OY18+TNn/vz5BON1Wyr1K3DqWWDUr8CoX4FRvwKjfh2TA9x86Aj3/301L6/fx47qdjxy9UA6JETVjVG/AhOK/TrldA7n3ATnXP8Gft4E9ppZRwD/bUEDT7EL6FJvuTOQ38C4vwL/EvhbEBEREQktae2i+NN3zuPXU/qzdHsRlzy+kLdWNxR/pKVq6pzoWcDN/vs3A282MOYzoKeZdTOzCOBa/+Mws571xl0BbGhiPSIiIiIhwcx3tcO3/+18slJjufuvK7h3xgoOHq4KdmlyBjQ1RD8MXGxmm4CL/cuYWYaZzQFwzlXjm6bxLrAeeM05t/bo483sczNbDXwD+EET6xEREREJKdnt4/j7naP44YRezF69h4mPL2RdYU2wy5ImOuWc6K/jnCsExjewPh+4tN7yHGBOA+M0fUNERERaPa8njB9M6ElO7/b88NWV/OazMg5EruMnl/QmKtwT7PLkNOiKhSIiIiLNZGCXRN7+twsYn+nl+UXbuOLJRazNPxjssuQ0KESLiIiINKPoCA839ovkxVvOo6i8iilPfcwz87dQU6vLZbQkCtEiIiIiQZDTO4337h3LhL7p/O87G7h22mJ2HigPdlnSSArRIiIiIkGSFBvB0zcM4bFrBrJhTwkTH1/Ia0t30pSL4UnzUIgWERERCSIz46ohnfnnvRfQv1MC97++mjtfXkZhaUWwS5OvoRAtIiIiEgI6J8Xwyu0jefDSvny4YR+XPP4R8zbsDXZZchIK0SIiIiIhIizMuH1sNrPuGUNqXATffXEpP39jDWUV1cEuTU6gEC0iIiISYvp0aMebd4/hjguzeWVJHpc98RHL84qCXZbUoxAtIiIiEoIivR5+NqkvM24fSVWN4+pncnnsvS+oqqkNdmmCQrSIiIhISBuRncI7917ANwd35ol5m7n6mVx2Fx8OdlltnkK0iIiISIiLjwrn0WsG8swNQ9i6r4zJv19E7pb9wS6rTVOIFhEREWkhJp3bkTfvHkNybAQ3/nEJf1y0TeeUDhKFaBEREZEWJLt9HP/4/hgm9E3jV2+t495XV3K4sibYZbU5CtEiIiIiLUxcpJdnbhjKfZf0ZtaqfP7lmVxdMryZKUSLiIiItEBhYcb3x/Xghe+cx66iciY/uYhFmzRPurkoRIuIiIi0YON6pzHr7vNJj4/iphc+ZdrCLZon3QwUokVERERauKzUWGZ+bzST+nfkv+ds4J5XVlBeqascnk0K0SIiIiKtQGyklyevH8wDk/owZ80erno6lx2FZcEuq9VSiBYRERFpJcyMOy/szou3DGfPwSNc8eTHLNi4L9hltUoK0SIiIiKtzNhe7Zl99/l0TIjiO39awlMfbtY86TNMIVpERESkFcpMiWHm90YzeUAGj7z7Bd/7y3JKKzRP+kxRiBYRERFppWIivPzu2kH8+2V9eXftl3zzqY/Ztl/zpM8EhWgRERGRVszMuO2CbF6+dQT7Syu44slFzNuwN9hltXgK0SIiIiJtwOgeqcy+53wyk2O4dfpSnpi7idpazZM+XQrRIiIiIm1E56QY/n7XaKYM6sRj72/kjpeXUXKkKthltUgK0SIiIiJtSFS4h8euGchDk/sxb0MBU576mM0FpcEuq8VRiBYRERFpY8yMW8Z04y+3jaC4vIopT33M++s0TzoQCtEiIiIibdTI7BRm33M+2e1juf2lpTz2/kbNk24khWgRERGRNiwjMZrX7hjF1UM788TcTdz+0lIOHtY86VNRiBYRERFp46LCPTxy9QB+deU5LNi4jylPfcymvSXBLiukKUSLiIiICGbGjaOyeGXqSEqOVDPlqY955/M9wS4rZClEi4iIiEid87KSeeue8+mZHs+dLy/nkXc3UKN50l+hEC0iIiIix+mQEMWrd4zkuuFdeOrDLXz3xc84WK550vUpRIuIiIjIV0R6PfzPVQP472+eS+6W/Vzx1CLNk66nSSHazJLN7H0z2+S/TTrJuIlm9oWZbTazBxrY/hMzc2aW2pR6REREROTMun5EJjOmjqK8soZv/WExy3YUBbukkNDUI9EPAHOdcz2Buf7l45iZB3gKmAT0A64zs371tncBLgbymliLiIiIiJwFQ7smMfOu0SRGh3PD85/w4RcFwS4p6Joaoq8EpvvvTwemNDBmOLDZObfVOVcJzPA/7qjfAvcDmrEuIiIiEqK6JMfw+l2j6ZEWx+3Tl/LGil3BLimozLnTz65mVuycS6y3XOScSzphzNXAROfcbf7lG4ERzrm7zewKYLxz7gdmth0Y5pzbf5LXmgpMBUhPTx86Y8aM0677dJWWlhIXF9fsr9tSqV+BU88Co34FRv0KjPoVGPUrMC25X4erHU8sP8L6A7Vc2zuCid3Cz/prBrNf48aNW+acG3bieu+pHmhmHwAdGtj0YCNf2xpY58wsxv8c32jMkzjnpgHTAIYNG+ZycnIa+fJnzvz58wnG67ZU6lfg1LPAqF+BUb8Co34FRv0KTEvv10U5Nfzw1ZXMWPMlCR0688DEPpg1FPnOjFDs1ylDtHNuwsm2mdleM+vonNtjZh2BhibI7AK61FvuDOQD3YFuwCp/0zsDy81suHPuywDeg4iIiIg0o0ivh99fN4Tk2M/5w4KtHCit5H+uOhevp+2c+O2UIfoUZgE3Aw/7b99sYMxnQE8z6wbsBq4FrnfOrQXSjg461XQOEREREQkdnjDjV1f2JzUuksc/2ERReSVPXj+EqHBPsEtrFk3958LDwMVmtgnfGTYeBjCzDDObA+CcqwbuBt4F1gOv+QO0iIiIiLRgZsa9E3rxqyn9mbuhgBv/+GmbuShLk45EO+cKgfENrM8HLq23PAeYc4rnympKLSIiIiISHDeO7EpyTAQ/fHUl1/xhMS/dOpz0dlHBLuusajsTV0RERETkrLlsQEdevOU8dhWVc9XTuWzdVxrsks4qhWgREREROSNG90hlxtRRHKmq4epnF7N6V3GwSzprFKJFRERE5Iw5t3MCr981mpgID9dN+4RFm1rnOSMUokVERETkjOqWGsvf7xpNl+QYbnlxCbNX5Qe7pDNOIVpEREREzrj0dlG8escoBndJ4t9mrGB67vZgl3RGKUSLiIiIyFmREB3OS7cOZ0LfdB6atZbH3t+Icy7YZZ0RCtEiIiIictZEhXt45oYhXDOsM0/M3cSD//icmtqWH6SbesVCEREREZGv5fWE8b//MoDUuEienr+ForJKfvvtQS366oYK0SIiIiJy1pkZ90/sQ2pcJL98ax1F5Ut47qZhxEeFB7u006LpHCIiIiLSbL57fjce//Yglm4v4tppn7CvpCLYJZ0WhWgRERERaVZTBnfi+ZuHsXVfGVc/m0teYXmwSwqYQrSIiIiINLuc3mn89fYRHDxcxVXP5LI2/2CwSwqIQrSIiIiIBMXgzCRev3MUER7j2j98wuIthcEuqdEUokVEREQkaHqkxfP6XaNJT4ji5j8t4Z3Pvwx2SY2iEC0iIiIiQZWRGM3f7hjFORnt+N5fljFjSV6wSzolhWgRERERCbqk2Aj+ctsIxvZqzwMz1/DkvE0hfXVDhWgRERERCQkxEV6eu2kY3xzcif97byO/mL2O2hC9uqEutiIiIiIiISPcE8aj3xpISmwEzy/aRmFZJVemh16QVogWERERkZASFmY8eFlfUuMjefifG9iaEsb5F9SE1GXCFaJFREREJOSYGXde2J3k2AjeWbKOSG9ozUJWiBYRERGRkHXNsC6klW7BzIJdynFCK9KLiIiIiLQACtEiIiIiIgFSiBYRERERCZBCtIiIiIhIgBSiRUREREQCpBAtIiIiIhIghWgRERERkQApRIuIiIiIBMicC71rkZ+Kme0DdgThpVOB/UF43ZZK/QqcehYY9Ssw6ldg1K/AqF+BUb8CE8x+dXXOtT9xZYsM0cFiZkudc8OCXUdLoX4FTj0LjPoVGPUrMOpXYNSvwKhfgQnFfmk6h4iIiIhIgBSiRUREREQCpBAdmGnBLqCFUb8Cp54FRv0KjPoVGPUrMOpXYNSvwIRcvzQnWkREREQkQDoSLSIiIiISIIVoEREREZEAKUQDZvaCmRWY2ecn2W5m9oSZbTaz1WY2pN62iWb2hX/bA81XdfA0ol83+Pu02sxyzWxgvW3bzWyNma00s6XNV3VwNaJnOWZ20N+XlWb2n/W26TP21e331evV52ZWY2bJ/m1t6jNmZl3M7EMzW29ma83sBw2M0T7Mr5H90j7Mr5H90v6rnkb2TPswPzOLMrMlZrbK369fNDAmNPdhzrk2/wOMBYYAn59k+6XAPwEDRgKf+td7gC1ANhABrAL6Bfv9hEC/RgNJ/vuTjvbLv7wdSA32ewjBnuUAbzWwXp+xU4+dDMyrt9ymPmNAR2CI/348sPHEz4j2YQH3S/uwwPql/VeAPTthfFvfhxkQ578fDnwKjDxhTEjuw3QkGnDOLQQOfM2QK4GXnM8nQKKZdQSGA5udc1udc5XADP/YVu1U/XLO5TrnivyLnwCdm6WwENaIz9jJ6DN2atcBr5zFckKac26Pc265/34JsB7odMIw7cP8GtMv7cOOaeTn62Ta3OcLTqtnbX0f5pxzpf7FcP/PiWe9CMl9mEJ043QCdtZb3uVfd7L1csyt+P71eJQD3jOzZWY2NUg1hapR/j9n/dPMzvGv02fsa5hZDDAR+Hu91W32M2ZmWcBgfEdy6tM+rAFf06/6tA/zO0W/tP9qwKk+Y9qH+ZiZx8xWAgXA+865FrEP8zbXC7Vw1sA69zXrBTCzcfh+AZ1fb/UY51y+maUB75vZBv9Rx7ZuOdDVOVdqZpcC/wB6os/YqUwGPnbO1T9q3SY/Y2YWh+8X8b3OuUMnbm7gIW16H3aKfh0do32Y3yn6pf1XAxrzGUP7MACcczXAIDNLBN4ws/7OufrfiQnJfZiORDfOLqBLveXOQP7XrG/zzGwA8DxwpXOu8Oh651y+/7YAeAPfn2LaPOfcoaN/znLOzQHCzSwVfcZO5VpO+DNoW/yMmVk4vl/Wf3HOzWxgiPZh9TSiX9qH1XOqfmn/9VWN+Yz5aR9Wj3OuGJiP7+h8fSG5D1OIbpxZwE3+b4eOBA465/YAnwE9zaybmUXg+59hVjALDQVmlgnMBG50zm2stz7WzOKP3ge+ATR49oW2xsw6mJn57w/H9/9mIfqMnZSZJQAXAm/WW9fmPmP+z80fgfXOucdOMkz7ML/G9Ev7sGMa2S/tv+pp5P+T2of5mVl7/xFozCwamABsOGFYSO7DNJ0DMLNX8H27ONXMdgEP4ZvYjnPuWWAOvm+GbgbKgVv826rN7G7gXXzfEH3BObe22d9AM2tEv/4TSAGe9u9Xq51zw4B0fH+mAd9n76/OuXea/Q0EQSN6djVwl5lVA4eBa51zDtBnrOF+AXwTeM85V1bvoW3xMzYGuBFY459TCPBzIBO0D2tAY/qlfdgxjemX9l/Ha0zPQPuwozoC083Mg+8fYK85594yszshtPdhuuy3iIiIiEiANJ1DRERERCRACtEiIiIiIgFSiBYRERERCZBCtIiIiIhIgBSiRUREREQCpBAtIiIiIhIghWgRERERkQD9f1bblzLUhhj1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "    a = 1.\n",
    "    b = 3.\n",
    "    u_0 = 2.\n",
    "    K = 1.\n",
    "    n = 20\n",
    "\n",
    "    (t, U) = explicitMidpoint(f_1, a, b, u_0, n, demoMode=True)\n",
    "    h = (b-a)/n\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Solving du/dt = Ku, {a=}, {u_0=}  by the Explicit Midpoint Method\")\n",
    "    plt.plot(t, u_1(t), 'g', label=\"Exact solution\")\n",
    "    plt.plot(t, U, 'b:', label=f\"Solution with h={h:0.3}\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Error\")\n",
    "    plt.plot(t, U - u_1(t))\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Observation:** The errors are very similar to those for the Explicit Trapezoid Method, not \"half as much and of opposite sign\" as seen with integration; the exercises give a hint as to why this is so."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "    a = 1.\n",
    "    b = a + 4 * np.pi  # Two periods\n",
    "    u_0 = 2.\n",
    "    K = 2.\n",
    "    n = 50\n",
    "\n",
    "    (t, U) = explicitMidpoint(f_2, a, b, u_0, n)\n",
    "    C = (u_0 - np.cos(a)) * np.exp(K*a)\n",
    "    h = (b-a)/n\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Solving du/dt = K(cos(t) - u) - sin(t), {K=}, {a=}, {u_0=} by the Explicit Midpoint Method\")\n",
    "    plt.plot(t, u_2(t), 'g', label=\"Exact solution\")\n",
    "    plt.plot(t, U, 'b:', label=f\"Solution with h={h:0.3}\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    \n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Error\")\n",
    "    plt.plot(t, U - u_2(t))\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Observation:** This time, the errors are slightly better than for the Explicit Trapezoid Method but still not \"half as much \" as seen with integration; this is because this equation has a mix of integration (the \"sin\" and \"cos\" parts) and exponential growth (the \"Ku\" part.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The \"Classical\", Fourth Order Accurate, Runge-Kutta Method\n",
    "\n",
    "This is the original Runge-Kutta method:\n",
    "\n",
    "$$\\begin{split}\n",
    "K_1 &= h f(t, u)\n",
    "\\\\\n",
    "K_2 &= h f(t + h/2, u + K_1/2)\n",
    "\\\\\n",
    "K_3 &= h f(t + h/2, u + K_2/2)\n",
    "\\\\\n",
    "K_4 &= h f(t + h, u + K_3)\n",
    "\\\\\n",
    "u(t+h) &\\approx u + \\frac{1}{6}(K_1 + 2 K_2 + 2 K_3 + K_4)\n",
    "\\end{split}$$\n",
    "\n",
    "This — or rather some variants to estimate and contol errors — is perhaps the most widely used general purpose method for numerical solution of ODE IVP's.\n",
    "\n",
    "The derivation of this is far more complicated than for the other methods above, and is omitted.\n",
    "For now, we will instead assess its accuracy \"*a postiori*\", through the next exercise and some examples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 4\n",
    "\n",
    "A) Verify that for the simple case where $f(t, u) = f(t)$,\n",
    "this gives the same result as the composite ximpson's Rule for integration.\n",
    "\n",
    "B) Do one step of this method for the canonical example $du/dt = ku$, $u(t_0) = u_0$.\n",
    "It will have the form $U_1 = G U_0$ where the growth factor $G$ approximates the factor $g=e^{kh}$ for the exact solution $u(t_1) = g u(t_0)$ of the ODE.\n",
    "\n",
    "C) Compare to the growth factors $G$ seen for previous methods, and to the growth factor $g$ for the exact solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def RungeKutta(f, a, b, u_0, n=100, demoMode=False):\n",
    "    \"\"\"Use the (classical) Runge-Kutta Method\n",
    "    to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "    u = np.empty_like(t)\n",
    "    u[0] = u_0\n",
    "    for i in range(n):\n",
    "        K_1 = f(t[i], u[i])*h\n",
    "        K_2 = f(t[i]+h/2, u[i]+K_1/2)*h\n",
    "        K_3 = f(t[i]+h/2, u[i]+K_2/2)*h\n",
    "        K_4 = f(t[i]+h, u[i]+K_3)*h\n",
    "        u[i+1] = u[i] + (K_1 + 2*K_2 + 2*K_3 + K_4)/6\n",
    "    return (t, u)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yet again, available for import with\n",
    "\n",
    "    from numerical_methods_module import RungeKutta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "    a = 1.\n",
    "    b = 3.\n",
    "    u_0 = 2.\n",
    "    K = 1.\n",
    "    n = 10\n",
    "\n",
    "    (t, U) = RungeKutta(f_1, a, b, u_0, n, demoMode=True)\n",
    "    h = (b-a)/n\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Solving du/dt = Ku, {a=}, {u_0=}  by the Runge-Kutta Method\")\n",
    "    plt.plot(t, u_1(t), 'g', label=\"Exact solution\")\n",
    "    plt.plot(t, U, 'b:', label=f\"Solution with h={h:0.3}\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Error\")\n",
    "    plt.plot(t, U - u_1(t))\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "    a = 1.\n",
    "    b = a + 4 * np.pi  # Two periods\n",
    "    u_0 = 2.\n",
    "    K = 2.\n",
    "    n = 50\n",
    "\n",
    "    (t, U) = RungeKutta(f_2, a, b, u_0, n)\n",
    "    C = (u_0 - np.cos(a)) * np.exp(K*a)\n",
    "    h = (b-a)/n\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Solving du/dt = K(cos(t) - u) - sin(t), {K=}, {a=}, {u_0=} by the Runge-Kutta Method\")\n",
    "    plt.plot(t, u_2(t), 'g', label=\"Exact solution\")\n",
    "    plt.plot(t, U, 'b:', label=f\"Solution with h={h:0.3}\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    \n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Error\")\n",
    "    plt.plot(t, U - u_2(t))\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"euler-redux\"></a>\n",
    "## For comparison: the above examples done with Euler's Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numerical_methods_module import euler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "    a = 1.\n",
    "    b = 3.\n",
    "    u_0 = 2.\n",
    "    K = 1.0\n",
    "    n = 40\n",
    "\n",
    "    (t, U) = euler(f_1, a, b, u_0, n)\n",
    "    h = (b-a)/n\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Solving du/dt = Ku, {a=}, {u_0=}\")\n",
    "    plt.plot(t, u_1(t), 'g', label=\"Exact solution\")\n",
    "    plt.plot(t, U, 'b:', label=f\"Euler's answer with h={h:0.3}\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Error\")\n",
    "    plt.plot(t, U - u_1(t))\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "    a = 1.\n",
    "    b = a + 4 * np.pi  # Two periods\n",
    "    u_0 = 2.\n",
    "    K = 2.\n",
    "    n = 50\n",
    "\n",
    "    (t, U) = euler(f_2, a, b, u_0, n)\n",
    "    C = (u_0 - np.cos(a)) * np.exp(K*a)\n",
    "    h = (b-a)/n\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Solving du/dt = K(cos(t) - u) - sin(t), {K=}, {a=}, {u_0=} by Euler's Method\")\n",
    "    plt.plot(t, u_2(t), 'g', label=\"Exact solution\")\n",
    "    plt.plot(t, U, 'b:', label=f\"Euler's answer with h={h:0.3}\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    \n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Error\")\n",
    "    plt.plot(t, U - u_2(t))\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "This work is licensed under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
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 },
 "nbformat": 4,
 "nbformat_minor": 4
}
