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   "source": [
    "# Predictor-Corrector Methods — Coming Soon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- Section 6.7 *Multistep Methods* in {cite}`Sauer`.\n",
    "- Section 5.6 *Multistep Methods* in {cite}`Burden-Faires`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "We have seen one predictor-corrector method already: the explicit trapezoid method, which uses Euler's method to *predict* a first approximation of the solution, and then *corrects* this using an approximation of the implicit trapezoid method.\n",
    "\n",
    "We will look at combining the $s$-step Adams-Bashforth and Adams-Moulton methods to achieive an two-stage, $s$-step method of same order of accuracy as the latter while being explicit — the explicit trapezoid method is this in the simplest case $s=1$."
   ]
  },
  {
   "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 matplotlib.pyplot import figure, plot, grid, title, xlabel, ylabel, legend"
   ]
  }
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