{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Initial Value Problems for ODEs, Part 6: A Very Brief Introduction to Multistep Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- Section 6.7 *Multistep Methods* of [Sauer](../references.html#Sauer)\n",
    "\n",
    "- Section 5.6 *Multistep Methods* of [Burden&Faires](../references.html#Burden-Faires)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "When approximating derivatives we saw that there is a distinct advantage in accuracy to using the centered difference approximation\n",
    "\n",
    "$$\\frac{df}{dt}(t) \\approx \\delta_h f(t) := \\frac{f(t+h) - f(t-h)}{2h}$$\n",
    "\n",
    "(with error $O(h^2)$) over the forward difference approximation\n",
    "\n",
    "$$\\frac{df}{dt}(t) \\approx \\Delta_h f(t) := \\frac{f(t+h) - f(t)}{h}$$\n",
    "\n",
    "(which has error $O(h)$).\n",
    "\n",
    "However Euler's method used the latter, and all ODE methods seen so far avoid using values at \"previous\" times like $t-h$.\n",
    "There is a reason for this, as using data from previous times introduces some complications, but sometimes those are worth overcoming, so let us look into this."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1: The Leap-frog method\n",
    "\n",
    "\n",
    "Inserting the above centered difference approximation of the derivative into the ODE $du/dt = f(t, u)$ gives\n",
    "\n",
    "$$\\frac{u(t+h) - u(t-h)}{h} \\approx f(t, u(t))$$\n",
    "\n",
    "which leads to the *leap-frog method*\n",
    "\n",
    "$$\\frac{U_{i+1} - U_{i-1}}{2h} = f(t_i, U_i)$$\n",
    "\n",
    "or\n",
    "\n",
    "$$U_{i+1} = U_{i-1} + 2 h f(t_i, U_i)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the first example of a multistep method:\n",
    "\n",
    "**Definition**:\n",
    "A *multistep method* for numerical solution of an ODE IVP $du/dt = f(t, u)$ is one of the form\n",
    "\n",
    "$$U_{i+1} = \\phi(U_i, \\dots U_{i-s+1}, h), \\quad s > 1 $$\n",
    "\n",
    "so that the new approximate value of $u(t)$ depends on approxiamt value at multiple previous times.\n",
    "\n",
    "More specifically, this is called an $s$-step method; this jargon is consistent with all methods seen in earlier sections being called *one-step methods*; for example,\n",
    "Euler's method can be written as\n",
    "\n",
    "$$U_{i+1} = \\phi_E(U_i, h) := U_i + h f(t_i, U_i)$$\n",
    "\n",
    "and the explicit midpoint method can be written as the one-liner\n",
    "\n",
    "$$U_{i+1} = \\phi_{EMP}(U_i, h) := U_i + h f(t_i+h/2, U_i + h f(t_i, U_i)/2) h$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The leap-frog method already illustrates two of the complications that arise with multistep methods:\n",
    "\n",
    "- The initial data $u(a) = u_0$ gives $U_0$, but then the above formula gives $U_1$ in terms of $U_0$ and the non-existent value $U_{-1}$; a different method is needed to get $U_1$.\n",
    "More generally, with an $s$-step methods, one needs to compute the first $s-1$ steps, up to $U_{s-1}$, by some other method.\n",
    "\n",
    "- Leap-frog needs a constant step size $h$; the strategy of error estimation and error control using variable step size is still possible with some multistep methods, but that is distinctly more complicated than we have seen with one-step methods, and is not addressed in these notes.\n",
    "\n",
    "Fortunately many differential equations can be handled wwell by choosing a suitable fixed step size $h$.\n",
    "Thus, in these notes, we work only with equal step sizes, so that our times are $t_i = a + i h$ and we aim for approximations\n",
    "$U_i \\approx u(a + ih)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Second order accuracy of the leap-frog method\n",
    "\n",
    "Using the fact that the centered difference approximation is second order accurate,\n",
    "one can verify that\n",
    "\n",
    "$$\\frac{u(t_{i+1}) - u(t_{i-1})}{2h} - f(t, u(t_i)) = O(h^2)$$\n",
    "\n",
    "(Alternatively one can get this by inserting quadratic Taylor polynomials centered at $t_i$, and their error terms.)\n",
    "\n",
    "The definition of local trunctation error needs to be extended slightly:\n",
    "it is the error $U_{i+1} - u(t_{i+1})$ when one starts with exact values for all previous steps;\n",
    "that is, assuming $U_j = u(t_j)$ for all $j\\leq i$.\n",
    "\n",
    "The above results then shows that the local truncation error in each step is $U_{i+1} - u(t_{i+1}) = O(h^3)$,\n",
    "so that the \"local truncation error per unit time\" is\n",
    "\n",
    "$$\\frac{U_{i+1} - u(t_{i+1})}{h} = O(h^2)$$.\n",
    "\n",
    "A theorem in the section on [Global Error Bounds for One Step Methods](ODE-IVP-3-error-results-one-step-methods.ipynb)\n",
    "says that when a one-step methods has local truncation error per unit time of $O(h^p)$ it also has global truncation error of the same order.\n",
    "The situation is a bit more complicated with multi-step methods, but loosely *if* the errors in a multistep method has local truncation $O(h^p)$ and it converges (i.e. the global error goes to zero at $h \\to 0$) then it does so at the expected rate of $O(h^p)$.\n",
    "But multi-step methode can fail to converge, even if the local truncation error is of high order!\n",
    "This is dealt with via the concept of *stability*; not considered here, but addressed in both references above and a topic for future expansion of these notes.\n",
    "\n",
    "So in particular, when the leap-frog method converges it is second order accurate, just like the centered difference approximation of $du/dt$ that it is built upon."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The speed advantage of multi-step methds like the leap-frog method\n",
    "\n",
    "This second order accuracy illustrate a major potential advantage of multi-step methods:\n",
    "whereas any one-step Runge-Kutta method that is second order accurate (such as the explicit trapezoid or explicit midpoint methods) require at least two evaluations of $f(t, u)$ for each time step, the leap-frog methods requires only one.\n",
    "\n",
    "More generally, for every $s$, there are $s$-step methods with errors $O(h^s)$ that require only one evaluation of $f(t, u)$ per time step — for example, the Adams-Bashforth methods, as seen at\n",
    "\n",
    "- https://en.wikipedia.org/wiki/Linear_multistep_method#Adams-Bashforth_methods\n",
    "\n",
    "- https://en.m.wikiversity.org/wiki/Adams-Bashforth_and_Adams-Moulton_methods\n",
    "\n",
    "- [Sauer](../references.html#Sauer) Section 6.7.1  and 6.7.2\n",
    "\n",
    "- [Burden&Faires](../references.html#Burden-Faires), Section 5.6\n",
    "\n",
    "In comparison, any *explicit* one-step method order $p$ require at least $p$ evaluations of $f(t, u)$ per time step.\n",
    "\n",
    "% (See the [Introduction to Implicit Methods](ODE-IVP-7-implicit-methods-intro.ipynb) for the distinction between explicit and implicit methods.)"
   ]
  },
  {
   "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, show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def leap_frog(f, a, b, U_0, U_1, nSteps):\n",
    "    nUnknowns = len(U_0)\n",
    "    t = np.linspace(a, b, nSteps+1)\n",
    "    U = np.zeros([nSteps+1, nUnknowns])\n",
    "    U[0] = U_0\n",
    "    U[1] = U_1\n",
    "    h = (b-a)/nSteps\n",
    "    for step in range(1, nSteps):\n",
    "        U[step+1] = U[step-1] + 2*h*f(t[step], U[step])\n",
    "    return (t, U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Demo with the (undamped) mass-spring system\n",
    "\n",
    "def f_mass_spring(t, u):\n",
    "    return np.array([ u[1], -(k/M)*u[0] - (D/M)*u[1]])\n",
    "M = 1.0\n",
    "k = 1.0\n",
    "D = 0.0\n",
    "U_0 = [1.0, 0.0]\n",
    "a = 0.0\n",
    "periods =32\n",
    "b = 2 * np.pi * periods\n",
    "#nSteps = 1000  # Very Good?!\n",
    "nSteps = 100*periods  # Good?\n",
    "#nSteps = 20  # OK\n",
    "\n",
    "# We need U_1, for now, get it with the Runge-Kutta method;\n",
    "# this is overkill for accuracy, but since only one step is needed, the cost is negligible.\n",
    "from numerical_methods_module import RungeKutta_system\n",
    "h = (b-a)/nSteps\n",
    "(t_1step, U_1step) = RungeKutta_system(f_mass_spring, a, a+h, U_0, n=1)\n",
    "U_1 = U_1step[-1]\n",
    "(t, U) = leap_frog(f_mass_spring, a, b, U_0, U_1, nSteps)\n",
    "\n",
    "y = U[:,0]\n",
    "#print(f\"t={t}\")\n",
    "#print(f\"y={y}\")\n",
    "figure(figsize=[12, 6])\n",
    "plot(t, y)\n",
    "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"
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  "language_info": {
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
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}
