{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Error Control and Variable Step Sizes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- Section 6.5 *Variable Step-Size Methods* in {cite}`Sauer`.\n",
    "- Section 5.5 *Error Control and the Runge-Kutta-Fehlberg Method* in {cite}`Burden-Faires`.\n",
    "- Section 7.3 in {cite}`Chenney-Kincaid`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Basic ODE Initial Value Problem\n",
    "\n",
    "We consider again the initial value problem\n",
    "\n",
    "$$\n",
    "\\frac{d u}{d t} = f(t, u) \\quad a \\leq t \\leq b, \\quad u(a) = u_0\n",
    "$$\n",
    "\n",
    "We now allow the possibility that $u$ and $f$ are vector-valued as in the section on\n",
    "[Systems of ODEs and Higher Order ODEs](ODE-IVP-4-system-higher-order-equations-python.ipynb),\n",
    "but omitting the tilde notation $\\tilde u$, $\\tilde f$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Error Control by Varying the Time Step Size $h_i$\n",
    "\n",
    "Recall the variable step-size version of Euler's method:\n",
    "\n",
    "```{prf:algorithm}\n",
    ":label: euler-variable-h\n",
    "\n",
    "Input: $f$, $a$, $b$, $n$ <br>\n",
    "\n",
    "$t_0 = a$\n",
    "<br>\n",
    "$U_0 = u_0$\n",
    "<br>\n",
    "$h = (b-a)/n$\n",
    "<br>\n",
    "for i in $[0, n)$:\n",
    "<br>\n",
    "$\\qquad$ Choose step size $h_i$ somehow!\n",
    "<br>\n",
    "$\\qquad$ $t_{i+1} = t_i + h_i$\n",
    "<br>\n",
    "$\\qquad$ $U_{i+1} = U_i + h_i f(t_i, U_i)$\n",
    "<br>\n",
    "end\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now consider how to choose each step size, by estimating the error in each step,\n",
    "and aiming to have error per unit time below some limit like $\\epsilon/(b-a)$, so that the global error is no more than about $\\epsilon$.\n",
    "\n",
    "As usual, the theoretical error bounds like $O(h_i^2)$ for a single step of Euler's method are not enough for quantitative tasks like choosing $h_i$,\n",
    "but they do motivate more practical estimates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A crude error estimate for Euler's Method: Richardson Extrapolation\n",
    "\n",
    "Starting at a point (t, u(t)), we can estimate the error in Euler's method approximato at a slightly later time $t_i + h$ by using two approximations of $U(t + h)$:\n",
    "- The value given by a step of Euler's method with step size $h$: call this $U^{h}$\n",
    "- The value given by taking two steps of Euler's method each with step size $h/2$: call this $U_2^{h/2}$,\n",
    "because it involves 2 steps of size $h/2$.\n",
    "\n",
    "The first order accuracy of Euler's method gives $e_h = u(t+h) - U^{h} \\approx 2(u(t+h) - U_2^{h/2})$,\n",
    "so that\n",
    "\n",
    "$$e_h \\approx \\frac{U_2^{h/2} - U^{h}}{2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step size choice\n",
    "\n",
    "What do we do with this error information?\n",
    "\n",
    "The first obvious ideas are:\n",
    "- Accept this step if $e_h$ is small enough, taking $h_i = h$, $t_{i+1} = t_i + h_i$, and $U_{i+1} = U^h$, but\n",
    "- reject it and try again with a smaller $h$ value otherwise; maybe halving $h$; but there are more sophisticated options too."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise A\n",
    "\n",
    "Write a formula for $U_h$ and $e_h$ if one starts from the point $(t_i, U_i)$, so that $(t_i + h, U^h)$ is the proposed value for the next point $(t_{i+1}, U_{i+1})$ in the approximate solution — but only if $e_h$ is small enough!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error tolerance \n",
    "\n",
    "One simple criterion for accuracy is that the estimated error in this step be no more than some overall upper limit on the error in each time step, $T$.\n",
    "That is, accept the step size $h$ if\n",
    "\n",
    "$$|e_h| \\leq T$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A crude approach to reducing the step size when needed\n",
    "\n",
    "If this error tolerance is not met, we must choose a new step size $h'$, and we can predict roughly its error behavior using the known order natue of the error in Euler's method: scaling dowen to $h' = s h$, the error in a single step scales with $h^2$ (in general it scales with $h^{p+1}$ for a method of order $p$), and so to reduce the error by the needed factor $\\displaystyle \\frac{e_h}{T}$ one needs approximately\n",
    "\n",
    "$$\n",
    "s^2 = \\frac{T}{|e_h|}\n",
    "$$\n",
    "\n",
    "and so using $e_h \\approx \\tilde{e}_h = |U^{h/2} - U^{h}|$ suggests using\n",
    "\n",
    "$$s = \\left( \\frac{T}{|U^{h/2} - U^{h}|} \\right)^{1/2}$$\n",
    "\n",
    "However this new step size might have error that is still slightly too large, leading to a second failure.\n",
    "Another is that one might get into an infinite loop of step size reduction.\n",
    "\n",
    "So refinements of this choice must be considered."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Increasing the step size when desirable\n",
    "\n",
    "If we simply follow the above aproach, the step size, once reduced, will never be increased.\n",
    "This could lead to great inefficiency, through using an unecessarily small step size just because at an earlier part of the time domain, accuracy required very small steps.\n",
    "\n",
    "Thus, after a successful time step, one might consider increasing $h$ for the next step.\n",
    "This could be done using exactly the above formula, but again there are risks, so again refinement of this choice must be considered.\n",
    "\n",
    "One problem is that if the step size gets too large, the error estimate can become unreliable; another is that one might need some minimum \"temporal resolution\", for nice graphs and such.\n",
    "\n",
    "Both suggest imposing an upper limit on the step size $h$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Another strategy for getting error estimates: two (related) Runge-Kutta methods\n",
    "\n",
    "The recurring strategy of estimating errors by the difference of two different approximations — one expected to be far better than the other — can be used in a nice way here.\n",
    "I will first illustrate with the simplest version, using Euler's Mathod and the Explicit Trapezoid Method.\n",
    "\n",
    "Recall that the increment in Euler's Method from time $t$ to time $t+h$ is\n",
    "\n",
    "$$K_1 = h f(t, U)$$\n",
    "\n",
    "whereas for the Explict Trapezoid Method it is $(K_1 + K_2)/2$, as given by\n",
    "\n",
    "$$\\begin{split}\n",
    "K_1 &= h f(t, U)\n",
    "\\\\\n",
    "K_2 &= h f(t+h, U + K_1)\n",
    "\\end{split}$$\n",
    "\n",
    "Thus we can use the difference, $|K_1 - (K_1 + K_2)/2| = |(K_1 - K_2)/2|$ as an error estimate.\n",
    "In fact to be cautious, one often drops the factor of $1/2$, so using approximation $\\tilde{e}_h = |K_1 - K_2|$.\n",
    "\n",
    "One has to be careful: this estimates the error in Euler's Method, and one has to use it that way:\n",
    "using the less accurate value $K_1$ as the update.\n",
    "\n",
    "A basic algorithm for the time step starting with $t_i, U_i$ is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:algorithm}\n",
    ":label: choose-step-size-1\n",
    "\n",
    "$K_1 \\leftarrow h f(t_i, U_i)$\n",
    "<br>\n",
    "$K_2 \\leftarrow h f(t_i + h, U_i + K_1)$\n",
    "<br>\n",
    "$e_h \\leftarrow |K_1 - K_2|$\n",
    "<br>\n",
    "$s \\leftarrow \\sqrt{T/e_h}$\n",
    "<br>\n",
    "if $e_h < T$\n",
    "<br>\n",
    "$\\quad U_{i+1} = U_i + K_1$\n",
    "<br>\n",
    "$\\quad t_{i+1} = t_i + h$\n",
    "<br>\n",
    "$\\quad$ Increase $h$ for the *next* time step:\n",
    "<br>\n",
    "$\\quad h \\leftarrow s h$\n",
    "<br>\n",
    "else: $\\quad$ (not good enough: reduce $h$ and try again)\n",
    "<br>\n",
    "$\\quad h \\leftarrow s h$\n",
    "<br>\n",
    "$\\quad$ Start again from $K_1 = \\dots$\n",
    "<br>\n",
    "end\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, in practice one needs:\n",
    "\n",
    "- An upper limit $h_{max}$ on the step size $h$, partly because error estimates become unreliable if $h$ gets too large,\n",
    "and also becuase subsequent use of the results (like graphs) might need sufficiently \"fine\" data.\n",
    "\n",
    "- A lower limit $h_{max}$ on $h$, to avoid infinite loops and such.\n",
    "\n",
    "- Since we are using only an approximation $\\tilde{e}_h$ of $e_h$, and out of general caution,\n",
    "it is typical to include a \"safety factor\" of about $0.8$ or $0.9$, when computing the *next* time step: reducing the step size scale factor to $S = 0.9 \\sqrt{T/e_h}$.\n",
    "\n",
    "Incorporating these refinements:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:algorithm}\n",
    ":label: choose-=step-size-2\n",
    "\n",
    "$K_1 = h f(t_i, U_i)$\n",
    "<br>\n",
    "$K_2 = h f(t_i+h, U_i + K_1)$\n",
    "<br>\n",
    "$e_{h} = |K_1 - K_2|$\n",
    "<br>\n",
    "$s = 0.9\\sqrt{T/e_h}$\n",
    "<br>\n",
    "if $e_h < T$\n",
    "<br>\n",
    "$\\quad U_{i+1} = U_i + K_1$\n",
    "<br>\n",
    "$\\quad t_{i+1} = t_i + h$\n",
    "<br>\n",
    "$\\quad$ Increase $h$ for the *next* time step:\n",
    "<br>\n",
    "$\\quad h \\leftarrow \\min(0.9 s h, h_{max})$\n",
    "<br>\n",
    "else: $\\quad$ (not good enough; reduce $h$ and try again)\n",
    "<br>\n",
    "$\\quad h \\leftarrow \\max(0.9 s h, h_{min})$\n",
    "<br>\n",
    "$\\quad$ Start again from $K_1 = \\dots$\n",
    "<br>\n",
    "end\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise B\n",
    "\n",
    "Implement the above, and test on the two familiar examples\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "du/dt &= Ku\n",
    "\\\\\n",
    "&\\text{and}\n",
    "\\\\\n",
    "du/dt &= K(\\cos(t) - u) - \\sin(t)\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "($K=1$ is enough.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Partial Solution to Exercise B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib.pyplot import figure, plot, title, grid\n",
    "\n",
    "# Get a \"stop watch\"\n",
    "# This gives the \"wall clock\" time in seconds since a reference moment, called \"the epoch\".\n",
    "# (For macOS and UNIX, the epoch is the beginning of 1970.)\n",
    "from time import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def euler_error_control(f, a, b, u_0, errorTolerance=1e-3, h_min=1e-6, h_max=0.1, steps_max=1000, demoMode=False):\n",
    "    # Use Python lists rather than Numpy arrays; they are easier to \"increment\"\n",
    "    # Initialize variables holding the current values of t and U\n",
    "    steps = 0\n",
    "    t_i = a\n",
    "    U_i = u_0\n",
    "    t = [t_i]\n",
    "    U = [U_i]\n",
    "    h = h_max  # Start optimistically!\n",
    "    while t_i < b and steps < steps_max:\n",
    "        K_1 = h*f(t_i, U_i)\n",
    "        K_2 = h*f(t_i + h/2, U_i + K_1/2)\n",
    "        errorEstimate = abs(K_1 - K_2)\n",
    "        s = 0.9 * np.sqrt(errorTolerance/errorEstimate)\n",
    "        if errorEstimate <= errorTolerance:  # Success!\n",
    "            t_i += h\n",
    "            U_i += K_1\n",
    "            t.append(t_i)\n",
    "            U.append(U_i)\n",
    "            # Adjust step size up, but not too big\n",
    "            h = min(s*h, h_max)\n",
    "        else:  #Innacurate; reduce step size and try again\n",
    "            h = max(s*h, h_min)\n",
    "            if demoMode: print(f\"{t_i=}: Decreasing step size to {h:0.3e} and trying again.\")\n",
    "        # A refinement not mentioned above; the next step should not overshoot t=b:\n",
    "        if t_i + h > b:\n",
    "            h = b - t_i\n",
    "        steps += 1\n",
    "    # Convert out to Numpy arrays, so that they can be used as input to numerical functions and such:\n",
    "    t = np.array(t)\n",
    "    U = np.array(U)    \n",
    "    return (t, U)\n",
    "    # Note: if the step count ran out, this does not reach t=b, but at least it is correct as far as it goes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(t, u):\n",
    "    return k*u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 1.\n",
    "a = 1.\n",
    "b = 3.\n",
    "u_0 = 2.\n",
    "def u(t):\n",
    "    \"\"\"Note: the input \"t\" must be a numpy array or a number; not a Python list.\"\"\"\n",
    "    return u_0*np.exp(k*(t-a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t_i=1.0: Decreasing step size to 9.000e-02 and trying again.\n",
      "\n",
      "With errorTolerance=0.01, this took 36 time steps, of average length 0.0556\n",
      "The maximum absolute error is 0.831\n",
      "The maximum absolute error per time step is 0.0231\n",
      "The time taken to solve was 0.000254 seconds\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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azy7Zrn8uy/PuJwQAAADAf1jhAwBBbtLQFI1KT1ReYVmDjaR/MT6jwfxOHSKUfU5n9Uo+tg+RaZp68uNtKq6o0bnd4pUYU7vZ9Oq8w/r46wPK6pGgC3qxGggAAABoLQQ+AAA57RFN3qNnePcEDe+e4DNW5fbohuHdtLmgRD2SorzjS7YW6unF21V4tNIn8Pnt2xvVJS5C1w1L8dl7iOPhAQAAgLODwAcAcMbCQqz6eSOrgQandNDk81J0fg+Hd+xIaZVeWrZTkjT5vG7e8Zm5GzR35S6Z4nh4AAAA4EwR+AAAWsyY3kka0zupwfhPxqZrf0mFosNqv4byXeV6deUu7/O1x8Nv1LDUBD3zyXb17xyryed1k9ViNHgtAAAAAA0R+AAAWlVcVKjuvqiXz9iOwtIG89ymqc+2HdS81bv136/DdMPwY6uB/rV6t4oranRxnyR1S4hqcC0AAAAQ7Ah8AAB+l+aIavR4+AxnjO66sKcshmQYx1b3vLx8p9btcaljbLg38NlbVK531+3ToK4dGuwxBAAAAAQbAh8AgN/VHQ8/M3ej3KbpPR5+aGqChqY2DG8uzXQqOTZcA7rYvWMrdxzSQx98rSHd4vTGD0d4x3O/2KMOkTYNS0vw3kIGAAAABDr+5AsAaBNOdjz88e4Y3aPBWHJMuC4b4FRfZ6x3zDRNzXr3K7nKq/Xvu0eqf+fagGjbgRJtO3BUA7p0UKcODX8eTgsDAABAe0fgAwBoM5pzPPzxRvR0aERPh89YebVbF2UkaVNBiXolR3vH/70+X4/+Z6uuHtxFf752oHd8wcYCbT1Qor8u3CKPyWlhAAAAaL8IfAAAASsyNER/mTSowXh8VKj6dYrVoJQO3rEjpVW64+XPfeZ5TGlG7gb1SorWOSlxPvsIAQAAAG2Zxd8FAADQ2n6Qlar37rlAU+qd/HWkrEo9kxqe+OUxpezZy/TMJ994x2rcHrnKqlulVgAAAOB0EPgAACCpe2K0/nnLebI0sojHakh9nDHex1/lF2vg7z7SVU//z2eeaZrHXwoAAAD4BYEPAADfqjstzPrtrVtWw9Afr87Ul78brxE9ju0PtGX/UUlSbLjN5/rrnl2uK578TOt2F7VazQAAAEBj2MMHAIB6mnJa2DXndtFFGUkqrjh2W1e126M1u4tUVeNRbMSxIOg/mw7olZV7dGlmR11/XrcGrwUAAAC0BAIfAACO05TTwuKiQhUXFep9HGIx9N/po7V+j0upCZGqqamRJK3MO6LPthWqe+Kx/YFM09TP3livnknRumF4N0WHNfw65mh4AAAAnAkCHwAAzgLDMNQ1PlJd4yN9xq8b0kW9kmPVu+OxY+H3HCnXG5/vUYjF0E0jUr3jH3+9X/muCrnKqvWnjzZzNDwAAABOG4EPAAAtqHtilHp36uAzFhFq1YxLM3S4tErhNqt3/NUVu/WfTftlSKrb/rnuaPhBXTuod8fYVqsbAAAA7RubNgMA0Moc0WG6fXQPzZjQx2d8WFqcMjvH6vizvjymdP1zK3zGjpRWcSoYAAAATojABwCANuK2UT307A+GNHo0/DkpcT6Pr3t2uYb8/j/6YteRVqoOAAAA7QmBDwAAbciJjoaffcNg75zyKrd2Hi7VodIqdY07tmdQ7hd7dM3spZq7cler1w0AAIC2hT18AABoY051NHxEqFXr7h+nzQUlSowJ844v235Iq3ce0bC0eO+Y22Pq129t1MAudl01uLPCQqwCAABA4CPwAQCgDTrV0fBhIVYN6NLBZ+yei3ppWFq8+nWye8c2F5Ro7spdenddiL43pKt3fPk3h2QxDA3oYvfZOFriSHgAAIBAQOADAECAaOxY+JjwEN05podqPKas9TYH+uvCLVqx47Aeys7UdcNqj3wvr3LrlRU79eD7mzgSHgAAoJ0j8AEAIIB1jY/Uz8dnNBjv3CFCiTFhOrfbsc2g3167V79/b5P3sceUZuZu1Kj0RFb6AAAAtDMEPgAABKG/TBrU4Fj39XuKGsxzm6amvrhKfZ2x+vn4DHW0h7dShQAAADgTnNIFAECQMgxDhnHsNq+7L+rV4Eh4iyF9XVCit9ftU3T4sX8nWrLloF5buUt7i8pbq1wAAAA0A4EPAACQ1PiR8L+7sr/+ecswPXB5X0WHHQt8Xl2xS7/M3aC31uz1jlXVeLT94NEGK4cAAADQ+rilCwAAeJ3oSPgLeiX6zDu3W5wOl1ZpRI8E79i6PUX63jPL1McZqw9+fEGr1g0AAABfBD4AAMDHqY6El6Rpo7pr2qjuPmM7D5UpNMSi7o4on/GpL65UZFiIfjqut9KOew4AAAAtg8AHAACcFdec20UTBzhVXF7tHSuuqNYnWw7KY0q/uayvd3zljsP6uqBYF/RK9IZA+a5y7SgsVZojilPBAAAAzhCBDwAAOGvCbVaF26zexxE2q167LUsb9rp8TvjK/WKPXlu1W7eN6q6ZE/po3qpdmpG7QR6zdqPonOxMTRqa4o+3AAAAEBAIfAAAQIuxWS0alhavYWnxPuMDunTQniPlGtnToXxXuTfskSSPKc3I3aBR6Yms9AEAADhNBD4AAKDVTT4vRZPPq13Bs3R7oTfsqeMxpbzCMjntEfr1WxtkMQxNPT+NPYAAAACaiGPZAQCAX6U5omQxfMeshqFUR6Qqa9ya//levbRspyqq3d7n8wpLtXLHYVXVeFq5WgAAgPaBwAcAAPiV0x6hnOxMWY3a1MdqGHowu7+c9ggZMvTodYM07YI0ZXSM8V4zd9UuXfu3ZfrNWxt9Xss0j1sqBAAAEKS4pQsAAPjdpKEpGpWeqLzCMqU6Ir1794SGWHRJv466pF9Hn/mhVosSokI1vMexvYEOllTqssc/1cheDj1yzUBZj182BAAAEEQIfAAAQJvgtEc0eZPmn4zrrfsuTpe73oqepdsLdaCkUl/nl/iEPblf7FFsuE1ZPRIUFcYffQAAQHDgTz0AAKBdslgMWXQs2LmkX0e9Ou08n319TNNUzgdf62BJpV6ddp5G9HBIksqqamSzWmSzWpTvKteOwlKlOaI4FQwAAAQMAh8AABAQwm1Wb6BTp7zarXF9k7U674jO7RbnHf/nsp164uNtGtEjQf/ZtF8eU7IYUk52piYNTWnt0gEAAM46Ah8AABCwIkND9IerMhuMf7HriI5W1mjhV/tVd1OYx5R+Ob/2CPirB3eRhT2AAABAO8YpXQAAIOjMvv5cPXhVfx1/ppcpKeeDTTLqZT2u8urWLA0AAOCsIPABAABBx2IxdGFGko5fxGNIunJgZxn1Ep/vPbNUYx5ZpI17Xa1bJAAAwBkg8AEAAEHJaY9QTnamrN+GO1bD0ENXZ+r+K/p55xw6WqkdhaXadbhMXeKObei8dFuhXlqWpz1Hylq9bgAAgKZgDx8AABC0Jg1N0aj0ROUVlinVEdnglK6E6DCt+e04bdjjUofIUO/43FW79e66fTpYUql7LuwuSfJ4TFXWuBUWYm3V9wAAANCYFl3hc+TIEU2ZMkV2u112u11TpkxRUVHRCedXV1frF7/4hTIzMxUVFaVOnTrpBz/4gfbt29eSZQIAgCDmtEcoq0fCCY9kjw4LUVaPBJ+xYWnxOi8tXhdmJHnHvsov0aBZC3XP3DUtWi8AAEBTtGjgM3nyZK1du1YLFizQggULtHbtWk2ZMuWE88vKyvTFF1/oN7/5jb744gvl5uZqy5YtuuKKK1qyTAAAgGaZMryb5t2epcEpx456X7bjkMqr3aqodvvM/efynVq6rVBVNR7vWL6rXEu3FyrfVd5qNQMAgODSYrd0bdq0SQsWLNDy5ct13nnnSZKee+45ZWVlafPmzerdu3eDa+x2uxYuXOgz9sQTT2jYsGHatWuXUlJSWqpcAACAM3Lr+aka3TtZZr2jv0oqqvW7d79UtdvU4p+OUaojSvNW7dKM3A3ymJLFkHKyMzVpKH/GAQAAZ1eLBT7Lli2T3W73hj2SNHz4cNntdi1durTRwKcxLpdLhmGoQ4cOjT5fWVmpyspK7+Pi4mJJtbeHVVe332NU62pvz+8BTUOvgwe9Di70O3jU9bimpkbpiZE+Y0WlFbp8gFO7Dpepsz1UuwpLvGGPJHlMaUbuBmWlxclpD/dL/Wg6PtfBhX4HD3odPAKh182p3TDN+v8OdfY8+OCDmjNnjrZs2eIznp6erqlTp2rGjBmnfI2KigqNHDlSGRkZevnllxud88ADD2jWrFkNxl999VVFRkaeXvEAAAAtYKvL0JNfNdzU+a6+bjkjTe0pNdQz1lQI56gCAIBGlJWVafLkyXK5XIqNjT3p3Gav8DlRwFLfqlWrJEnGt8ec1meaZqPjx6uurtZ1110nj8ejp59++oTzZsyYoenTp3sfFxcXq2vXrho3btwp33xbVl1drYULF2rs2LGy2Wz+LgctiF4HD3odXOh38GhOr/NdFXp60xLvCh+p9rauaydcqMVbDmr2O5uU1T1eL00d0sJV43TwuQ4u9Dt40OvgEQi9rrurqSmaHfjcdddduu666046JzU1VevXr9f+/fsbPHfw4EElJyef9Prq6mpde+212rFjhz7++OOTBjdhYWEKCwtrMG6z2dptA+sLlPeBU6PXwYNeBxf6HTya0usUh0052ZmambtRbtOU1TD0YHZ/pThiZG45JEd0mEb2SvS+To3box+9+oWyuifoumEpCrdx5HtbwOc6uNDv4EGvg0d77nVz6m524ONwOORwOE45LysrSy6XSytXrtSwYcMkSStWrJDL5dKIESNOeF1d2LN161YtWrRICQkJJ5wLAADQ3kwamqJR6YnKKyxTqiPSexz8jSNSNWV4N1W5j53m9fnOI/rwy/1aseOwbhjezTt+uLRKcZG2Jq2aBgAAwanF7hDv06ePxo8fr2nTpmn58uVavny5pk2bpokTJ/ps2JyRkaE333xTUu1mh9dcc41Wr16tV155RW63WwUFBSooKFBVVVVLlQoAANCqnPYIZfVI8IY9dSwWw2cVT5ojSr+a0EfTLuiuEOuxP7bd+o9VOv+hj7Vyx+FWqxkAALQvLXZKlyS98soruueeezRu3DhJ0hVXXKEnn3zSZ87mzZvlcrkkSXv27NE777wjSRo0aJDPvEWLFmnMmDEtWS4AAECbkhQbrmmjuvuMHa2s0Zb9R3W0skYp8ccOqFi/p0g7Cks1pneS7BHtc5k6AAA4e1o08ImPjz/h6Vp16h8SlpqaqhY6NAwAACAgRIeFaPWvL9ba3UXqWO8o95eX79Trq/fophGpeuCKfj7X5LvKtaOwVGmOqAarigAAQGBq0cAHAAAAZ1+4zarh3X33OeyeGK2eSdEa2/fY4Rg7Cks1+bnlKnBVyFTtiWA52ZmaNDSllSsGAACtjcAHAAAgANwxuofuGN3DZ7X0/M93K99V4X3sMaWZuRuVnhyjQV07sOkzAAABrMU2bQYAAEDrqx/iZHbp0OB5t2nq+88u15g/LVZBvTAIAAAEFgIfAACAADWgi12W4xbxWAzJlKnqGo+SY8O8459uPag1u46wnyIAAAGCwAcAACBAOe0RysnOlPXbVT9Ww1BOdqa++M04PX/jUJ/VQL//9yZd9fRSvbNun7/KBQAAZxF7+AAAAASwSUNTNCo9UXmFZUp1RHpP6erbKdY7p6Lard4dY7S/pEJj0pO84//dtF+fbi3UVed01sCuHVq7dAAAcAYIfAAAAAKc0x5x0uPYw21WPf79c1Tj9ijEemwB+Buf79EHGwsUGWr1Bj6macpjStbj7xUDAABtCrd0AQAAQJJ8wh5J+v6wFF09uIsmDujkHfsqv1jD/vAfzXr3y9YuDwAANAMrfAAAANCoUemJGpWe6DP20Zf7dai0SvuKyn3GN+xxKcMZo8KjldpRWKo0R9RJVxUBAICWReADAACAJrvrOz01JDVO0WHH/hjpKq9W9uz/KcRiUWWNWx6z9jSwnOxMTRqa4sdqAQAIXgQ+AAAAaDKb1aILevmu+tlRWKroMJuOlFV5xzymNCN3g+IibRrbt6PPiWAAAKDlsYcPAAAAzsigrh30xPfPaTDuMaXb/vmFFn613w9VAQAQ3Ah8AAAAcMZ6JEXp+IO7DEmJ0WE++wAt/Gq/nlq0TXuOlLVugQAABBkCHwAAAJwxpz1COdmZsn5765bVMPTQ1ZlaPvMihdus3nlzlu7QIx9u1ttr9/mrVAAAggJ7+AAAAOCsmDQ0RaPSE5VXWKZUR2Sjp3RdOaizTFO6vN5R75/vPKzH/rtNk4Z01WUDnK1ZMgAAAYvABwAAAGeN0x5x0uPYrx3SVdcO6eoz9taafVqy5aASo8N8Ap8at0chVhakAwBwOgh8AAAA4Fe3jEyTIzpM5/dM8I4dKK7QJY8u0bi+HfWHq/oT/AAA0EwEPgAAAPCrVEeUfnxxL5+xD7/aryNl1dp6oMQn7NlXVC6nPVwFxRXaUViqNEfUSVcUAQAQrAh8AAAA0OZcPyxFvZKi5TFN71i126OJT3wmQ9KRsip5TMliSDnZmZo0NMV/xQIA0AYR+AAAAKDNsVgMDe+e4DO2ZX+JSiurVVlzLATymNKM3A06JyVO6ckxrV0mAABtFjdDAwAAoF3o18mu2Tec22DcY0oTHvtUH3+93w9VAQDQNhH4AAAAoN3o44yVxWg4bpqmBnTp4H28/eBRbd1f0nqFAQDQxhD4AAAAoN1w2iOUk50pq1Gb+lgNQw9lZ+rjn46RIzrMO+/Jj7dp7F+X6KlF2/xVKgAAfsUePgAAAGhXJg1N0aj0ROUVlinVEdnglC7TNOX2mAqxGBrR49g+QAWuCn2V79KoXokc8w4ACHgEPgAAAGh3nPaIEx7HbhiGHv/+Obr/8r6Kjwr1js9btVt//c8WTcjsqKevb7gXEAAAgYR/2gAAAEBASogOk2Ec2/AnzGZRfFSoxvZN9o5VVLv10rI8HS6t8keJAAC0GFb4AAAAICjcMbqHbj4/zWfswy8L9Nu3v9SL/8vTxz8Z7RMQSVK+q1w7CkuV5oiSI5I/OgMA2g++tQAAABA0QkN8F7hHhoaof+dYfScj2Rv2mKappxdvV1WNR098vFUeU7IY0u+v7KsofxQNAMBpIPABAABA0BrbN1lj+yarxu3xjm3cW6xHPtzsM89jSr9++yvdf05rVwgAwOlhDx8AAAAEvfqndoVYDZ2XFtdgjseU1h82ZJpma5YGAMBpIfABAAAA6unjjNWj150ji9Hwufl5Vm09cLT1iwIAoJkIfAAAAIDjOO0RysnOlPXbfX0shnRuSgf1ivUoPTnGO+/9Dflatv0Qq34AAG0Oe/gAAAAAjZg0NEWj0hOVV1imVEekHJEheu+9973P17g9euCdL3WgpFLP/WCIz3HvAAD4G4EPAAAAcAJOe4Sc9ghJUnV1teqf2l5a6dZFfZL1v22FGp2e6B1f/s0h1bhNjeiRIEtj94UBANAKCHwAAACA02CPtCknO1NujylrvWDnTx9u1uqdR/TbiX1188g0P1YIAAhm7OEDAAAAnIH6YU+N26O+nWIVF2nTxAFO7/iW/SX6ZMtBeTzs9QMAaB0EPgAAAMBZEmK16HdX9tfKX12spNhw7/izS77RjX9fqd+/t6nBNfmuci3dXqh8V3lrlgoACHDc0gUAAACcZTar77+rOqLDFBseossGdPSOHSyp1FOLtuqlZTvlMWtPAsvJztSkoSmtXS4AIACxwgcAAABoYb+8NEMrf3WxBqfEecde+OwbzVlaG/ZIkseUZuZuZKUPAOCsIPABAAAAWkG4zSqj3jFfxeXVDea4TVMffblfpslePwCAM0PgAwAAAPjB3Rf10vGntlsM6f53vtRNL67yT1EAgIBB4AMAAAD4gdMeoZzsTFm/XfVjNQxd2t+psBCLBnSx+8wtcFX4o0QAQDvGps0AAACAn0wamqJR6YnKKyxTqiNSTnuEjpRWqd6dX9qUX6wJj3+qsX2S9cwN58py/LIgAAAaQeADAAAA+JHTHiGnPcL7OC4q1Of5ZdsPyTQlW4jFJ+ypqvEoNIQF+wCAxhH4AAAAAG3YzSPTNKZ3oupv41xUVqXv/PkTXdKvo+6/vK/CbVa/1QcAaJsIfAAAAIA2rntitM/jDzYW6HBpldbtLlIYq3wAAI0g8AEAAADameuGdlWaI0puj+k96t3tMXXt35bpgl4O3XpBd0WH1f5RP99Vrh2FpUpzRPncOgYACGwEPgAAAEA7YxiGhndP8BlbvPmAPt95RNsPHtUdo3tIkuat2qUZuRvkMWuPfM/JztSkoSn+KBkA0MoIfAAAAIAAcEGvRD123SCVVroVbrMq31XuDXskyWNKM3M3alR6Iit9ACAIEPgAAAAAASA0xKIrB3X2Pt5RWOoNe+q4TVN5hWUEPgAQBNjhDQAAAAhAaY4o1TvFXZJkNQylOiL17rp92rq/xD+FAQBaBYEPAAAAEICc9gjlZGfK+u2mzlbD0IPZ/RUZGqJfzF+vsX9dog17XH6uEgDQUrilCwAAAAhQk4amaFR6ovIKy5TqiJTTHqG9ReUa1StROw+XqX/nWO/c7QePqktchMJCrH6sGABwthD4AAAAAAHMaY/w2bOnc4cIPTPlXFXWuL1Huns8pm6Zs0pHK9164cYhGti1g5+qBQCcLdzSBQAAAASh+it59hwpV2WNR1U1bvVMivaOV7s9/igNAHAWsMIHAAAACHIpCZFa8vMLtXX/UUWFHfsrwu3//FySNOPSDPVKjvFXeQCA08AKHwAAAACyWS3q2+nYnj4Frgot3nxAizYfkM3KXxsAoL1hhQ8AAACABjraw/XxT8Zo6fZDSnVEecefWrRNkjR5WIriokKV7yrXjsJSpTmifPYKAgD4F4EPAAAAgEalOqJ8wp7iimrNXrxdRytr1K9TrPYXV2hG7gZ5TMliSDnZmZo0NMWPFQMA6rA2EwAAAECTRNis+v13+2viAKfSk6O9YY8keUxpZu5G5bvK/VskAEASgQ8AAACAJrJZLfruOZ315OTByjtU5g176rhNU3mFZf4pDgDgg8AHAAAAQLOlOaJkMXzHLIaU6oiUJB0prZL7+EQIANBqCHwAAAAANJvTHqGc7ExZjdrUp24Pn7qNm3/2xnpd/JdPtOKbQ/4sEwCCFps2AwAAADgtk4amaFR6ovIKy5TqiPSGPa6yan2+87CKyqvliAnzc5UAEJwIfAAAAACcNqc9osFx7PZImz77xXe0dPsh9UiM9o4/tWibKqvduun8NMVHhbZ2qQAQVAh8AAAAAJx1UWEhGts32fu4uKJazyzerpLKGmV26eDzHADg7GMPHwAAAAAtLio0RA9fM0BXDOykizKSvOOr8g5r6/4SP1YGAIGJFT4AAAAAWpzVYujSTKcuzXR6xzweUzNyN2jbgaN6+vrBmlDvOQDAmWGFDwAAAAC/KKmoUY/EKNkjbLqgl8M7frSyRqZpKt9VrqXbC5XvKvdjlQDQPrHCBwAAAIBf2CNt+tuUIXKVVSsm3OYd/8nra7Vhr0v5rgqZ5rEj3ycNTfFjtQDQvrDCBwAAAIBf2SOPhT1HSqu0ZMtB7SuqDXskyWNKM3M3stIHAJqBwAcAAABAmxEXFapHrzunwbjbNPXS0p2qcXv8UBUAtD8EPgAAAADalAFd7LIYDcdnf7JdizYfbP2CAKAdatHA58iRI5oyZYrsdrvsdrumTJmioqKiJl9/++23yzAMPfrooy1WIwAAAIC2xWmPUE52pqxGbepjMaTx/ZM1vHu8z5Huuw+XqZoVPwDQqBbdtHny5Mnas2ePFixYIEm67bbbNGXKFL377runvPatt97SihUr1KlTp5YsEQAAAEAbNGloikalJyqvsEypjkg57REyTVPGtyGQx2Pqln+sUkW1R09fP1j9O9v9XDEAtC0tFvhs2rRJCxYs0PLly3XeeedJkp577jllZWVp8+bN6t279wmv3bt3r+666y59+OGHuuyyy1qqRAAAAABtmNMeIac9wvu4LuyRpF2Hy3ToaJWqajzqGhfpj/IAoE1rscBn2bJlstvt3rBHkoYPHy673a6lS5eeMPDxeDyaMmWKfvazn6lfv36n/HkqKytVWVnpfVxcXCxJqq6uVnV19Rm+C/+pq709vwc0Db0OHvQ6uNDv4EGvgwe9bls620P18fSR+rrgqCJtx/qS88FmpTmilH1OJ4WGnP4OFvQ7eNDr4BEIvW5O7S0W+BQUFCgpKanBeFJSkgoKCk543R//+EeFhITonnvuadLPk5OTo1mzZjUY/+ijjxQZ2f6T/oULF/q7BLQSeh086HVwod/Bg14HD3rd9ry/sfZ/C8qkF9dZZcpQSd56dY4689em38GDXgeP9tzrsrKyJs9tduDzwAMPNBqw1Ldq1SpJvksu69S/7/Z4n3/+uR577DF98cUXJ5xzvBkzZmj69Onex8XFxeratavGjRun2NjYJr1GW1RdXa2FCxdq7Nixstls/i4HLYheBw96HVzod/Cg18GDXrd9FdVuWTrv0Y7CUk27vK93fOPeYvVKjlZYM1b80O/gQa+DRyD0uu6upqZoduBz11136brrrjvpnNTUVK1fv1779+9v8NzBgweVnJzc6HWffvqpDhw4oJSUFO+Y2+3WT37yEz366KPKy8trcE1YWJjCwsIajNtstnbbwPoC5X3g1Oh18KDXwYV+Bw96HTzoddtls9k0bVRPn7GSimrd9I/PFWGz6rXbhivVUbvsJ99Vrh2FpUpzRPnsE9TYa9Lv4ECvg0d77nVz6m524ONwOORwOE45LysrSy6XSytXrtSwYcMkSStWrJDL5dKIESMavWbKlCm6+OKLfcYuueQSTZkyRVOnTm1uqQAAAACC3I7CUkXYrIoKs6prfO2WD/NW7dKM3A3ymLVHvudkZ2rS0JRTvBIAtC8ttodPnz59NH78eE2bNk1/+9vfJNUeyz5x4kSfDZszMjKUk5Ojq666SgkJCUpISPB5HZvNpo4dO570VC8AAAAAaMyALh20+GdjtK+oXFaLoXxXuTfskSSPKc3M3ahR6YknXekDAO3N6W9b3wSvvPKKMjMzNW7cOI0bN04DBgzQP//5T585mzdvlsvlaskyAAAAAASxcJtV3ROjJdWu+KkLe+q4TVN5hU3fCBUA2oMWW+EjSfHx8Xr55ZdPOsc0zZM+39i+PQAAAABwOtIcUbIY8gl9rIahVEekNuxxqX/n2CYfIAMAbVmLrvABAAAAgLbEaY9QTnamrN+GOlbD0IPZ/VVa6daVT32mK578n8qqavxcJQCcuRZd4QMAAAAAbc2koSkalZ6ovMIypToi5bRH6L31+YqwWZUcG67I0BBVV1f7u0wAOCMEPgAAAACCjtMe4bNJ82UDnBrePV7l1W7vWKVbmv6v9bp9dE/172z3R5kAcNq4pQsAAAAAJCVEh6lLXKT38Sf5ht5dX6C7566R5/idngGgjWOFDwAAAAA0YlCCKUtcR43t55TFUrvnj2maOlBSqeTYcD9XBwAnxwofAAAAAGhEUoT0l+8N0BUDO3nHFm0+oAv+uEgPffC1HysDgFMj8AEAAACAJlq8+aCq3B6Z4hYvAG0bt3QBAAAAQBP97sr+uqRfR/V1xnrHdh0q07vr92nq+alylVdrR2Gp0hxRPptCA0BrI/ABAAAAgGY4v6fD5/Gj/9mi3DV79dGXBdqw1yWPKVkMKSc7U5OGpvipSgDBjlu6AAAAAOAMjO6dqM4dwrX+27BHkjymNDN3g/Jd5f4tDkDQIvABAAAAgDNw5aDO+uPVA2Uet62P25Q++rLAP0UBCHoEPgAAAABwhnokRenbk9t9VFR5Wr8YABCBDwAAAACcMac9QjnZmbIatamPxZAu7pOkW0d1987ZdqBEB0oq/FUigCDDps0AAAAAcBZMGpqiUemJyissU6oj0ueULo/H1E9eX6etB47qqcmDdWFGkh8rBRAMCHwAAAAA4Cxx2iMaPY79SFmVZBgyJPXvbG/9wgAEHQIfAAAAAGhhCdFheuvOEdp+8KgSY8K847MXb1dGxxiN6Z0ow2hkEyAAOE3s4QMAAAAArcAwDPVMivE+3nbgqP700WZNnbNKX+4r9mNlAAIRK3wAAAAAwA8So8N0y8g07S0q97nNq6rGo9AQ/m0ewJkh8AEAAAAAP7BH2jRzQh+ZpukdK6uq0SWPLtGETKd+fFEvRYbyVzYAp4fYGAAAAAD8qP7ePf9en6/dh8v1/oZ8WS214/muci3dXqh8V7m/SgTQDhEXAwAAAEAb8b1zuyghKlRWi6GwEKvmrdqlGbkb5DEliyHlZGdq0tAUf5cJoB0g8AEAAACANsIwDF3UJ1lS7cqeurBHkjymNDN3g0alJzZ69DsA1MctXQAAAADQBu0oLPWGPXXcppRXWOafggC0KwQ+AAAAANAGpTmiZDF8x6yGoVRHpPYVlev5T79RVY3HP8UBaPMIfAAAAACgDXLaI5STnSnrt5s6Ww1DD2b3l9MeoYc++Fq/f2+Tfpm73s9VAmir2MMHAAAAANqoSUNTNCo9UXmFZUp1RHr37hnZ06Hl3xzSzeen+blCAG0VgQ8AAAAAtGFOe0SDTZqvHdpVV57TSWEhVu/Yy8t3akdhqe65qJfsEbbWLhNAG0PgAwAAAADtUP2wp6SiWo98uFmu8mr1TIrW94dxdDsQ7NjDBwAAAADauZhwmx7//jm6bIBT1w7p6h2vqHb7sSoA/sQKHwAAAAAIAKPTEzU6PdH72OMx9f3nlqtThwj9dmJfJceG+7E6AK2NFT4AAAAAEIDW7SnSut1FWvz1ARmnng4gwLDCBwAAAAAC0Dkpcfr33Rdo+8GjSqq3umfjXpfio2zKO1SmNEdUgw2hAQQGAh8AAAAACFB9O8Wqb6dY7+Ot+0t0+ZOfyTRrH1sMKSc7U5OGsskzEGi4pQsAAAAAgsSybw55wx5J8pjSzNyNyneV+68oAC2CwAcAAAAAgkTPpOgGY27T1CvLd8rjMRu5AkB7ReADAAAAAEEizREly3E7OBuSnly0XXe/tsYvNQFoGQQ+AAAAABAknPYI5WRnymrUpj5Ww9DEgU5Fhlp1WabTz9UBOJvYtBkAAAAAgsikoSkalZ6ovMIypToi5bRHqPBopRKiQr1zVnxzSPtLKnX5AKcMg0PdgfaIwAcAAAAAgozTHuFzHLsjOsz7/ytr3Jrx5gZ9c7BUh49W6qbz0/xRIoAzxC1dAAAAAAAvQ4auGtRZXeIilH1uF3+XA+A0EfgAAAAAALxCQyy6+6Je+vgnYxQbbvOOP/Lh1/roywI/VgagObilCwAAAADQQGjIsfUBn+88rKcWbZck/Wf6KPVMivFXWQCaiMAHAAAAAHBSfZyxunNMD5VU1BD2AO0EgQ8AAAAA4KQiQ0P08/EZMk3TO1ZUVqVb/7FaP764ly7olejH6gA0hj18AAAAAABNUv+I9qcXb9fqnUf0f//+Sm6PqXxXuZZuL1S+q9yPFQKowwofAAAAAECz3fWdnqp2e3RJv4564/PdmpG7QR5TshhSTnamJg1N8XeJQFBjhQ8AAAAAoNliw226//J+6pYQ6Q17JMljSjNyN7DSB/AzAh8AAAAAwGnbUVjqDXvqeEwpr7DMPwUBkETgAwAAAAA4A2mOKFkM3zGLIaU6IiVJVTUeP1QFgMAHAAAAAHDanPYI5WRnyvrths5Ww1BOdqac9giZpqk7Xv5c981bq0NHK/1cKRBc2LQZAAAAAHBGJg1N0aj0ROUVlinVESmnPUKS9OW+Yi3afEA2i0U/urCnEqLD/FwpEDwIfAAAAAAAZ8xpj/AGPXX6d7brzTvP1+aCYvVMivaOV1S7FW6ztnaJQFDhli4AAAAAQIsZ1LWDzxHte46UaeQfP9azS7bLffxuzwDOGgIfAAAAAECreW3lbhUerdLCr/bLOPV0AKeJW7oAAAAAAK3mJ+PSlRIfqcHd4mT59ngvt8dUVY1HEaHc5gWcLazwAQAAAAC0GsMwdO3Qrj57+sxZmqdxj36i/20r9GNlQGAh8AEAAAAA+I3bY2ruyl3afbhceYdK/V0OEDC4pQsAAAAA4DdWi6G3fnS+5q3are/X29zZVVat0qpq5R0qU5ojqsEJYABOjsAHAAAAAOBX0WEhumVkmvex22Pqsic+1Z4j5ZIkiyHlZGf6nPYF4OS4pQsAAAAA0KYs3nzAG/ZIkseUZuZuVL6r/CRXAaiPwAcAAAAA0KY0dlqX2zS1uaDED9UA7ROBDwAAAACgTUlzROnbE9u9LIZ0z9w1enn5Tpmm6Z/CgHaEwAcAAAAA0KY47RHKyc6U1ahNfayGoaGp8SquqNFnWzm6HWgKNm0GAAAAALQ5k4amaFR6ovIKy5TqiFRyTLj+uXynJmQ6ZXwbBFW7PbIahizHLwcCQOADAAAAAGibnPYIn+PYbxyR6vP8Xxdu0bo9Rfrj1QPUJS6ylasD2jYCHwAAAABAu1NUVqWXlu3U0coafbmvmMAHOA6BDwAAAACg3ekQGap37x6p9zfk65J+Hb3jHo/JLV6A2LQZAAAAANBOpTmi9KMLe3ofl1e5dcVTn+mVFZzkBRD4AAAAAAACwmurdmnj3mI98d9tOlpZ4+9yAL/ili4AAAAAQEC4MStVpin1SIpWTLjNO26apvdkLyBYEPgAAAAAAAKCxWLo5pFpPmP/21ao2Yu3a/rYXqqo8SjNEeVz8hcQqAh8AAAAAAAByeMx9cA7X2rrgaP637ZCmZIshpSTnalJQ1P8XR7QotjDBwAAAAAQkCwWQ3+4qr8kqW4LZ48pzczdqHxXuf8KA1pBiwY+R44c0ZQpU2S322W32zVlyhQVFRWd8rpNmzbpiiuukN1uV0xMjIYPH65du3a1ZKkAAAAAgABU42l4WpfbNDVv1W4/VAO0nhYNfCZPnqy1a9dqwYIFWrBggdauXaspU6ac9Jrt27dr5MiRysjI0OLFi7Vu3Tr95je/UXh4eEuWCgAAAAAIQGmOKFka2a/50f9s1bYDR1u/IKCVtNgePps2bdKCBQu0fPlynXfeeZKk5557TllZWdq8ebN69+7d6HW/+tWvNGHCBD388MPese7du7dUmQAAAACAAOa0RygnO1MzczfKbZqyGNKY9CT1dsaoZ1K0qqur/V0i0CJaLPBZtmyZ7Ha7N+yRpOHDh8tut2vp0qWNBj4ej0fvvfeefv7zn+uSSy7RmjVrlJaWphkzZui73/1uoz9PZWWlKisrvY+Li4slSdXV1e36g1tXe3t+D2gaeh086HVwod/Bg14HD3odXOh3YMke5FRWWpx2HS5TSnyknPbaO0jq/t5YWi099p8tumNMT4WFsNVtoAqEz3VzajdM02x4Q+NZ8OCDD2rOnDnasmWLz3h6erqmTp2qGTNmNLimoKBATqdTkZGR+v3vf68LL7xQCxYs0MyZM7Vo0SKNHj26wTUPPPCAZs2a1WD81VdfVWRk5Nl7QwAAAACAgPTiFovWHrLonASPbkr3+Lsc4ITKyso0efJkuVwuxcbGnnRus1f4nChgqW/VqlWSJMNoeKOkaZqNjku1K3wk6corr9R9990nSRo0aJCWLl2qZ555ptHAZ8aMGZo+fbr3cXFxsbp27apx48ad8s23ZdXV1Vq4cKHGjh0rm83m73LQguh18KDXwYV+Bw96HTzodXCh38Gjurpa6w//R/uqQnX/tYPVr1P7/XskTi4QPtd1dzU1RbMDn7vuukvXXXfdSeekpqZq/fr12r9/f4PnDh48qOTk5EavczgcCgkJUd++fX3G+/Tpo88++6zRa8LCwhQWFtZg3GaztdsG1hco7wOnRq+DB70OLvQ7eNDr4EGvgwv9Dg4D4k3dd90oRUcc+7vl0u2F6pYQpc4dIvxYGVpCe/5cN6fuZgc+DodDDofjlPOysrLkcrm0cuVKDRs2TJK0YsUKuVwujRgxotFrQkNDNXToUG3evNlnfMuWLerWrVtzSwUAAAAAoEnq791T4KrQD1/+Qh7T1Nxpw9W/s92PlQGnp8V2o+rTp4/Gjx+vadOmafny5Vq+fLmmTZumiRMn+mzYnJGRoTfffNP7+Gc/+5nmzZun5557Ttu2bdOTTz6pd999V3feeWdLlQoAAAAAgFe126M0R5RSE6LUu2OMv8sBTkuLbj/+yiuvKDMzU+PGjdO4ceM0YMAA/fOf//SZs3nzZrlcLu/jq666Ss8884wefvhhZWZm6vnnn9f8+fM1cuTIliwVAAAAAABJUtf4SL1xR5ZeuGmIbNbavzabpqmNe12nuBJoO1rsWHZJio+P18svv3zSOY0dEnbzzTfr5ptvbqmyAAAAAAA4qRCrRUkx4d7H81bt1i9zN+j20d0149I+yneVa0dhqdIcUXLa2ecHbU+LBj4AAAAAAASCHYWlkqT4yFDNW7VLM3I3yGNKFkPKyc7UpKEpfq4Q8EXgAwAAAADAKcyY0Edj+yaroz1cox5eJM+3N6t4TGlm7kaNSk9kpQ/alBbdwwcAAAAAgEAxJDVeuw6XecOeOm7TVF5hmX+KAk6AwAcAAAAAgCZKc0TJYviOWQwp1RHpn4KAEyDwAQAAAACgiZz2COVkZ8pq1KY+dXv4cDsX2hr28AEAAAAAoBkmDU3RqPRE5RWWKdUR6Q17th88qhm5G/RQdqa6J0b7uUoEO1b4AAAAAADQTE57hLJ6JPis7HngnS+1csdhPfj+Jj9WBtQi8AEAAAAA4Cx45JqBurR/R/3hqkx/lwIQ+AAAAAAAcDZ0tIdr9g3nKjk23Ds2b9Uurdtd5L+iELQIfAAAAAAAaAHrdhfpV29u1NWzl+rrgmJ/l4Mgw6bNAAAAAAC0gNSEKI3tmyyLYah3coy/y0GQIfABAAAAAKAF2CNtevr6wapye2R8e4x7VY1H6/YUaWhqvJ+rQ6Djli4AAAAAAFqIYRgKC7F6H//po8363jPL9MR/t/qxKgQDAh8AAAAAAFqBaZoqr3JLktI7HrvFK99VrqXbC5XvKvdXaQhA3NIFAAAAAEArMAxD//fd/rpuWFf162SXVHuK14zcDfKYksWQcrIzNWloip8rRSBghQ8AAAAAAK2oLuzJd5V7wx5J8pjSzNyNrPTBWUHgAwAAAACAH+woLPWGPXXcpqm8wjL/FISAQuADAAAAAIAfpDmiZDF8x6yGoVRHpH8KQkAh8AEAAAAAwA+c9gjlZGfK+u2R7VbD0IPZ/bWjsFS/fXujKmvcfq4Q7RmbNgMAAAAA4CeThqZoVHqi8grLlOqIVIeIUI1+ZJEOlFQqISpMP764l79LRDtF4AMAAAAAgB857RFy2iO8j/94zQA9+8k3um1Udz9WhfaOwAcAAAAAgDbkwt5JGpOeKMM4tsHPgo0FuqhPkmxWdmZB0/A7BQAAAACANqZ+2PP22r264+XPdf3zK1Tt9vixKrQnBD4AAAAAALRhYSFWxYSFaFhqPCt80GTc0gUAAAAAQBs2vn9H9e8c67PPT1lVjcJCrLIef6478C2iQQAAAAAA2rgucZHecMc0Tf34tbW66cWVOnS00s+Voa1ihQ8AAAAAAO3I1gNH9dnWQrk9pvYVVSghOszfJaENIvABAAAAAKAdSU+O0dt3na+vC0qU2cXu73LQRnFLFwAAAAAA7Ux6coyuGNjJ+3hfUbl+8vo6bdlfoqXbC5XvKvdjdWgLWOEDAAAAAEA7Zpqmpr++Vsu/Oaz5X+yRJFkMKSc7U5OGpvi5OvgLK3wAAAAAAGjHDMPQ7aN6+Ix5TGlm7kZW+gQxAh8AAAAAANq5MFvDv967TVPb9h/1QzVoCwh8AAAAAABo59IcUfr21HYff/pos1zl1a1fEPyOwAcAAAAAgHbOaY9QTnamrEZt6mMxpLAQi+KiQhUdxva9wYiuAwAAAAAQACYNTdGo9ETlFZYp1RGp8iq3EqLCZP126Y9pmpJq9/xB4CPwAQAAAAAgQDjtEXLaIxp97qlF27T7cLlmXdlP4TZrK1eG1kbgAwAAAABAgNt9uEyP/merajymLsxI1Pj+Tn+XhBZG4AMAAAAAQIDrGh+pv980VP/bXkjYEyTYtBkAAAAAgCAwKj1RMy7t431cWePWW2v2evf2QWAh8AEAAAAAIMiYpqnfvvWl7p23Vve/86W/y0ELIPABAAAAACAI9e4Yo1CrRRf3SfZ3KWgB7OEDAAAAAECQMQxDN49M04RMpzraw73jFdVuTvAKEKzwAQAAAAAgSNUPe46UVumSR5fo6cXbtK+oTEu3FyrfVe7H6nAmWOEDAAAAAAD01tq92nmoTM9/ukN/+nCzPKZkMaSc7ExNGpri7/LQTKzwAQAAAAAAumlEqn4xPkNHyqrk+fbgLo8pzczdyEqfdojABwAAAAAAyDAMDexq1/GntLtNU3mFZf4pCqeNwAcAAAAAAEiS0hxRshgNxwuPVrR+MTgjBD4AAAAAAECS5LRHKCc7U1ajNvUxJHWLj9S4fh39WxiajU2bAQAAAACA16ShKRqVnqi8wjJ1S4hQbESowkKOHdVeXuVWRChHt7d1rPABAAAAAAA+nPYIZfVIUKcOkYoOO7ZW5JUVO3XpY0u07UCJH6tDUxD4AAAAAACAU6qscev5T3co71CZFn51wN/l4BS4pQsAAAAAAJxSWIhVb9yRpddW7dYdo7v7uxycAit8AAAAAABAkyREh+lHF/aU8e2mzm6PqTn/26HKGrefK8PxCHwAAAAAAMBpefjDr/XAu1/p1n+slmma/i4H9RD4AAAAAACA0zKih0Ox4SG6dkhX76oftA3s4QMAAAAAAE7L6PRELfn5heoQGeodq6xx+xzjDv9ghQ8AAAAAADht9cOe0soaXfXUUj358VZu8fIzVvgAAAAAAICz4r0N+foqv1gHSip03bAUVbs92lFYqjRHlJz2CH+XF1QIfAAAAAAAwFlx7ZCuqnGb6t0xWv/dtF8zcjfIY0oWQ8rJztSkoSn+LjFocEsXAAAAAAA4ayafl6JOHSK8YY8keUxpZu5G5bvK/VtcECHwAQAAAAAAZ9WOwlJv2FPHbZrKKyzzT0FBiMAHAAAAAACcVWmOKFmOO6XdYkipjkj/FBSECHwAAAAAAMBZ5bRHKCc7U1ajNvWp28OnbuNmTvBqeWzaDAAAAAAAzrpJQ1M0Kj1ReYVlSnVEesOeBRvzlfvFXj163SBFhhJLtBR+ZQEAAAAAQItw2iN8jmM/WlmjX+ZuUFFZtV5atlN3jO7hx+oCG7d0AQAAAACAVhEdFqIXbhyq7MGddevINH+XE9BY4QMAAAAAAFrNud3idG63OO9j0zS1eX+JMjrG+rGqwMMKHwAAAAAA4DezP9muyx7/TK+u2OXvUgIKgQ8AAAAAAPAL0zT1zcFSuT2majwef5cTULilCwAAAAAA+IVhGHrkmgG6fGAnjU5P9Hc5AYUVPgAAAAAAwG8Mw/AJe6pqPJr17pc6WFLpx6raPwIfAAAAAADQZvzhva/04v/yNOWFFfJ4TH+X024R+AAAAAAAgDbjxhGp6p4YpRkT+shiMSRJ+a5yLd1eqHxXuZ+raz9aNPA5cuSIpkyZIrvdLrvdrilTpqioqOik1xw9elR33XWXunTpooiICPXp00ezZ89uyTIBAAAAAEAb0T0xWh/eO8p7m9e8Vbt0/kMfa/JzK3T+Qx9r3ipO82qKFg18Jk+erLVr12rBggVasGCB1q5dqylTppz0mvvuu08LFizQyy+/rE2bNum+++7T3XffrbfffrslSwUAAAAAAG2EzVobV+S7yjUjd4Pq7uzymNLM3I2s9GmCFgt8Nm3apAULFuj5559XVlaWsrKy9Nxzz+nf//63Nm/efMLrli1bphtvvFFjxoxRamqqbrvtNg0cOFCrV69uqVIBAAAAAEAbtKOwVMdv4+M2TeUVlvmnoHakxQKfZcuWyW6367zzzvOODR8+XHa7XUuXLj3hdSNHjtQ777yjvXv3yjRNLVq0SFu2bNEll1zSUqUCAAAAAIA2KM0RpW+38fG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      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "errorTolerance = 1e-2\n",
    "time_start = time()\n",
    "(t, U) = euler_error_control(f, a, b, u_0, errorTolerance, demoMode=True)\n",
    "time_end = time()\n",
    "time_elapsed = time_end - time_start\n",
    "\n",
    "steps = len(U) - 1\n",
    "h_ave = (b-a)/steps\n",
    "U_exact = u(t)\n",
    "U_error = U-U_exact\n",
    "U_max = max(abs(U_error))\n",
    "print()\n",
    "print(f\"With {errorTolerance=}, this took {steps} time steps, of average length {h_ave:0.3}\")\n",
    "print(f\"The maximum absolute error is {U_max:0.3}\")\n",
    "print(f\"The maximum absolute error per time step is {U_max/steps:0.3}\")\n",
    "print(f\"The time taken to solve was {time_elapsed:0.3} seconds\")\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "title(f\"Solution to du/dt={k}u, u({a})={u_0}\")\n",
    "plot(t, U, \".:\")\n",
    "grid(True)\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "title(f\"Error in the above\")\n",
    "plot(t, U_error, \".:\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t_i=1.0: Decreasing step size to 2.846e-02 and trying again.\n",
      "\n",
      "With errorTolerance=0.001, this took 119 time steps, of average length 0.0168\n",
      "The maximum absolute error is 0.265\n",
      "The maximum absolute error per time step is 0.00223\n",
      "The time taken to solve was 0.000433 seconds\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "errorTolerance = 1e-3\n",
    "time_start = time()\n",
    "(t, U) = euler_error_control(f, a, b, u_0, errorTolerance, demoMode=True)\n",
    "time_end = time()\n",
    "time_elapsed = time_end - time_start\n",
    "\n",
    "steps = len(U) - 1\n",
    "h_ave = (b-a)/steps\n",
    "U_exact = u(t)\n",
    "U_error = U-U_exact\n",
    "U_max = max(abs(U_error))\n",
    "print()\n",
    "print(f\"With {errorTolerance=}, this took {steps} time steps, of average length {h_ave:0.3}\")\n",
    "print(f\"The maximum absolute error is {U_max:0.3}\")\n",
    "print(f\"The maximum absolute error per time step is {U_max/steps:0.3}\")\n",
    "print(f\"The time taken to solve was {time_elapsed:0.3} seconds\")\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "title(f\"Solution to du/dt={k}u, u({a})={u_0}\")\n",
    "plot(t, U, \".:\")\n",
    "grid(True)\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "title(f\"Error in the above\")\n",
    "plot(t, U_error, \".:\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t_i=1.0: Decreasing step size to 9.000e-03 and trying again.\n",
      "\n",
      "With errorTolerance=0.0001, this took 380 time steps, of average length 0.00526\n",
      "The maximum absolute error is 0.084\n",
      "The maximum absolute error per time step is 0.000221\n",
      "The time taken to solve was 0.00127 seconds\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "errorTolerance = 1e-4\n",
    "time_start = time()\n",
    "(t, U) = euler_error_control(f, a, b, u_0, errorTolerance, demoMode=True)\n",
    "time_end = time()\n",
    "time_elapsed = time_end - time_start\n",
    "\n",
    "steps = len(U) - 1\n",
    "h_ave = (b-a)/steps\n",
    "U_exact = u(t)\n",
    "U_error = U-U_exact\n",
    "U_max = max(abs(U_error))\n",
    "print()\n",
    "print(f\"With {errorTolerance=}, this took {steps} time steps, of average length {h_ave:0.3}\")\n",
    "print(f\"The maximum absolute error is {U_max:0.3}\")\n",
    "print(f\"The maximum absolute error per time step is {U_max/steps:0.3}\")\n",
    "print(f\"The time taken to solve was {time_elapsed:0.3} seconds\")\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "title(f\"Solution to du/dt={k}u, u({a})={u_0}\")\n",
    "plot(t, U, \".:\")\n",
    "grid(True)\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "title(f\"Error in the above\")\n",
    "plot(t, U_error, \".:\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(etmec)=\n",
    "## The explicit trapezoid method with error control\n",
    "\n",
    "In practice, one usually needs at least second order accuracy, and one approach to that is using computing a \"candidates\" for the next time step with a second order accurate Runge-Kutta method and also a third order accurate one, the latter used only to get an error estimate for the former.\n",
    "\n",
    "Perhaps the simplest of these is based on adding error estimation to the Explicit Trapezoid Rule.\n",
    "Omitting the step size adjustment for now, the main ingredients are:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:algorithm}\n",
    ":label: trapezoid-step-size\n",
    "\n",
    "$K_1 = h f(t, U)$\n",
    "<br>\n",
    "$K_2 = h f(t + h, U + K_1)$\n",
    "<br>\n",
    "(So far, as for the explicit trapezoid method)\n",
    "\n",
    "$K_3 = h f(t + h/2, U + (K_1 + K_2)/4)$\n",
    "<br>\n",
    "(a midpoint approximation, using the above)\n",
    "\n",
    "$\\delta_2 = (K_1 + K_2)/2$\n",
    "<br>\n",
    "(The order 2 increment as for the explicit trapezoid method)\n",
    "\n",
    "$\\delta_3 = (K_1 + 4 K_3 + K_2)/6$\n",
    "<br>\n",
    "(An order 3 increment — note the resemblance to Simpson's Rule for integration.\n",
    "This is only used to get the final error estimate below)\n",
    "\n",
    "$e_h = |\\delta_2 - \\delta_3 |, \\, = |K_1 -2 K_3 + K_2|/3$\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, if this step is accepted, one uses the explicit trapezoid rule step: $U_{i+1} = U_i + \\delta_2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step size adjustment\n",
    "\n",
    "The scale factor $s$ for step size adjustment must be modified for a method order $p$ (with $p=2$ now):\n",
    "- Changing step size by a factor $s$ will change the error $e_h$ in a single time step by a factor of about $s^{p+1}$.\n",
    "\n",
    "- Thus, we want a new step with this rescaled error of about $s^{p+1} e_h$ roughly matching the tolerance $T$.\n",
    "Equating would give $s^{p+1} e_h = T$, so $s = (T/e_h))^{1/(p+1)}$,\n",
    "but as noted above, since we are using only an approximation $\\tilde{e}_h$ of $e_h$\n",
    "it is typical to include a \"safety factor\" of about $0.9$, so something like\n",
    "\n",
    "$$s = 0.9 \\left( \\frac{T}{|\\tilde{e}_h|} \\right)^{1/(p+1)}$$\n",
    "\n",
    "Thus for this second order accurate method, we then get\n",
    "\n",
    "$$s = 0.9 \\left( \\frac{3 T}{|K_1 -2 K_3 + K_2|} \\right)^{1/3}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**A variant: relative error control**\n",
    "\n",
    "One final refinement: it is more common in software to impose a *relative error* bound: aiming for $|e_h/u(t)| \\leq T$,\n",
    "or $|e_h| \\leq T|u(t)|$.\n",
    "Approximating $u(t)$ by $U_i$, this changes the step size rescaling guideline to\n",
    "\n",
    "$$s = 0.9 \\left| \\frac{T U_i}{\\tilde{e}_h} \\right|^{1/(p+1)}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise C\n",
    "\n",
    "Implement {ref}`etmec`, and test on the two familiar examples\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "du/dt &= K u\n",
    "\\\\\n",
    "&\\text{and}\n",
    "\\\\\n",
    "du/dt &= K(\\cos(t) - u) - \\sin(t)\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "($K=1$ is enough.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fourth order accurate methods with error control: Runge-Kutta-Felberg and some newer refinements\n",
    "\n",
    "The details involve some messy coefficients; see the references above for those.\n",
    "\n",
    "The basic idea is to devise a fifth order accurate Runge-Kutta method such that we can also get a fourth order accurate method from the same colection of *stages* $K_i$ values.\n",
    "One catch is that any such fifth order method requires six stages (not five as you might have guessed).\n",
    "\n",
    "The first such method, still widely used, is the\n",
    "[Runge-Kutta-Felberg Mathod](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta%E2%80%93Fehlberg_method)\n",
    "published by Erwin Fehlberg in 1970:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:algorithm} RUnge-Kutta-Fehlberg\n",
    ":label: rkf\n",
    "\n",
    "$K_1 = h f(t, U)$\n",
    "<br>\n",
    "$K_2 = f(t + \\frac{1}{4}h, U + K_1/4)$\n",
    "<br>\n",
    "$K_3 = f(t + \\frac{3}{8} h, U + \\frac{3}{32} K_1 + \\frac{9}{32} K_2)$\n",
    "<br>\n",
    "$K_4 = f(t + \\frac{12}{13} h, U + \\frac{1932}{2197} K_1 - \\frac{7200}{2197} K_2 + \\frac{7296}{2197} K_3)$\n",
    "<br>\n",
    "$K_5 = f(t + h, U + \\frac{439}{216} K_1 - 8  K_2 + \\frac{3680}{2565} K_3  - \\frac{845}{4104} K_4)$\n",
    "<br>\n",
    "$K_6 = f(t + \\frac{1}{2}h, U - \\frac{8}{27} K_1 + 2 K_2 - \\frac{3544}{513} K_3 + \\frac{1859}{4104} K_4 - \\frac{11}{40} K_5)$\n",
    "<br>\n",
    "$\\delta_4 = \\frac{25}{216} K_1 + \\frac{1408}{2565} K_3 + \\frac{2197}{4104} K_4 - \\frac{1}{5} K_5$\n",
    "<br>\n",
    "(The order 4 increment that will actually be used)\n",
    "\n",
    "$\\delta_5 = \\frac{16}{135} K_1 + \\frac{6656}{12825} K_3 + \\frac{28561}{56430} K_4 - \\frac{9}{50} K_5  + \\frac{2}{55} K_6$\n",
    "<br>\n",
    "(The order 5 increment, used only to get the following error estimate)\n",
    "\n",
    "$\\tilde{e}_h = \\frac{1}{360} K_1 - \\frac{128}{4275} K_3 + \\frac{2197}{75240} K_4 + \\frac{1}{50} K_5  + \\frac{2}{55} K_6$\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This method is typically used with the relative error control mentioned above, and since the order is $p=4$,\n",
    "the recommended step-size rescaling factor is\n",
    "\n",
    "$$\n",
    "s = 0.9 \\left| \\frac{T U_i}{\\tilde{e}_h} \\right|^{1/5},\n",
    "= 0.9 \\left| \\frac{T U_i}{\\frac{1}{360} K_1 - \\frac{128}{4275} K_3 + \\frac{2197}{75240} K_4 + \\frac{1}{50} K_5  + \\frac{2}{55} K_6} \\right|^{1/5},\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ODE solvers in Python package SciPy \n",
    "\n",
    "Newer software often uses a variant called the [Dormand–Prince method](https://en.wikipedia.org/wiki/Dormand%E2%80%93Prince_method) published in 1980;\n",
    "for example this is the default method in the module `scipy.integrate` within Python package SciPy.\n",
    "This is similar in form to \"R-K-F\", but has somewhat smaller errors.\n",
    "\n",
    "The basic usage is\n",
    "\n",
    "    ode_solution = scipy.integrate.solve_ivp(f, [a, b], y_0)\n",
    "    \n",
    "because the output is an \"object\" containing many items; the ones we need for now are t and y,\n",
    "extracted with\n",
    "\n",
    "    t = ode_solution.t\n",
    "    y = ode_solution.y\n",
    "\n",
    "This defaut usage is synonymous with\n",
    "\n",
    "    ode_solution = scipy.integrate.solve_ivp(f, [a, b], y_0, method=\"RK45\")\n",
    "    \n",
    "where \"RK45\" refers to the Dormand–Prince method.\n",
    "Other options include `method=\"RK23\"`, which is second order accurate, and very similar to the above {ref}`etmec`\n",
    "\n",
    "Notes:\n",
    "- SciPy's notation is $dy/dt= f(t, y)$, so the result is called `y`, not `u`\n",
    "- The initial data `y_0` must be in a list or numpy array, even if it is a single number.\n",
    "- The output `y` is a 2D array, even if it is a single equation rather than a system.\n",
    "- This might output very few values; for more output times (for better graphs?), try something like\n",
    "\n",
    "`t_plot = np.linspace(a, b)`\n",
    "\n",
    "`[t, y] = solve_ivp(f, [a, b], y_0, t_eval=t_plot)`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get an ODE IVP solve function, from module \"integrate\" within package \"scipy\"\n",
    "from scipy.integrate import solve_ivp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To read more about this SciPy function scipy.integrate.solve_ivp,\n",
    "run the folowing help command in the notebook version of this section:\n",
    "\n",
    "    help(solve_ivp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(t, u):\n",
    "    return u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 0.0\n",
    "b = 2.0\n",
    "y_0 = [1.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time take to solve: 0.00107 seconds\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_plot = np.linspace(a, b)\n",
    "time_start = time()\n",
    "ode_solution = solve_ivp(f, [a, b], y_0, t_eval=t_plot)\n",
    "time_end = time()\n",
    "time_elapsed = time_end - time_start\n",
    "print(f\"Time take to solve: {time_elapsed:0.3} seconds\")\n",
    "\n",
    "# The output is an \"object\" containing many items; the ones we need for now are t and y.\n",
    "# More precisely \"y\" is a 2D array (just as y_0 is always an array)\n",
    "# though with only a single row for this example, so we just want the 1D array y[0]\n",
    "# These are extracted as follows:\n",
    "t = ode_solution.t\n",
    "y = ode_solution.y[0]\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "plt.title(\"Computed Solution\")\n",
    "plt.plot(t, y, \".:\")\n",
    "grid(True)\n",
    "\n",
    "y_exact = np.exp(t)\n",
    "errors = y - y_exact\n",
    "figure(figsize=[14,5])\n",
    "plt.title(\"Errors\")\n",
    "plt.plot(t, errors, \".:\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time take to solve: 0.00872 seconds\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Increase accuracy requirement.\n",
    "# \"rtol\" is a relative error tolerance, defaulting to 1e-3\n",
    "# \"atol\" is an absolute error tolerance, defaulting to 1e-3\n",
    "# It solve to the less demanding of these two,\n",
    "# so both must be specified to increase accuracy.\n",
    "\n",
    "t_plot = np.linspace(a, b)\n",
    "\n",
    "time_start = time()\n",
    "ode_solution = solve_ivp(f, [a, b], y_0, t_eval=t_plot, rtol=1e-12, atol=1e-12)\n",
    "time_end = time()\n",
    "time_elapsed = time_end - time_start\n",
    "print(f\"Time take to solve: {time_elapsed:0.3} seconds\")\n",
    "\n",
    "t = ode_solution.t\n",
    "y = ode_solution.y[0]\n",
    "figure(figsize=[14,5])\n",
    "plt.title(\"Computed Solution\")\n",
    "plt.plot(t, y, \".:\")\n",
    "grid(True)\n",
    "\n",
    "y_exact = np.exp(t)\n",
    "errors = y - y_exact\n",
    "figure(figsize=[14,5])\n",
    "plt.title(\"Errors\")\n",
    "plt.plot(t, errors, \".:\")\n",
    "grid(True);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
