09: Concept 7

Week 5/9 Ordinary Differential Equations.ipynb

@@ -730,7 +730,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 10,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -747,8 +747,38 @@
    },
    "outputs": [],
    "source": [
-    "# YOUR CODE HERE\n",
-    "raise NotImplementedError()"
+    "def ODEF(x, y):\n",
+    "    # TODO: Docstring.\n",
+    "    return np.array([y[1], -np.sin(y[0])])\n",
+    "\n",
+    "h   = .02\n",
+    "x   = np.arange(0, 2, h)\n",
+    "y   = (x + 1)**2 - 0.5*np.exp(x)\n",
+    "eta = np.zeros(len(x))\n",
+    "\n",
+    "fig = plt.figure(figsize=(12, 8))\n",
+    "gs = gridspec.GridSpec(2, 1, height_ratios=[2, 1])\n",
+    "\n",
+    "ax0 = plt.subplot(gs[0])\n",
+    "ax0.plot(x, y, label=\"exact solution\")\n",
+    "ax0.set_yscale(\"log\")\n",
+    "ax0.set_title(\"Solutions to $y' = y - x^2 + 1.0$\")\n",
+    "\n",
+    "\n",
+    "ax1 = plt.subplot(gs[1])\n",
+    "ax1.set_ylabel(\"$\\delta(x) = |\\~y(x) - y(x)|$\")\n",
+    "\n",
+    "\n",
+    "for alg, alg_name in algos:\n",
+    "    eta = integrator(x, y0, ODEF, alg)\n",
+    "    ax0.plot(x, eta, label=alg_name)\n",
+    "    ax1.plot(x, np.abs(eta - y), label=alg_name)\n",
+    "\n",
+    "ax0.legend()\n",
+    "plt.xlabel(\"x\")\n",
+    "ax0.set_ylabel(\"y(x)\")\n",
+    "ax1.legend()\n",
+    "plt.show()"
    ]
   }
  ],