09: Draft task 6

Week 5/9 Ordinary Differential Equations.ipynb

@@ -497,6 +497,7 @@
     "    phi = (1/12)*( 23*f(x[i - 1], y[i - 1]) - 16*f(x[i - 2], y[i - 2]) + 5*f(x[i - 3], y[i - 3]) )\n",
     "    return phi\n",
     "\n",
+    "# TODO: AB4 looks a bit off in the plots in task 5.\n",
     "def phi_ab4(x, y, f, i):\n",
     "    # The first three y values are to be calculated using the Runga-Kutta method.\n",
     "    if i < 4:\n",
@@ -651,8 +652,31 @@
    },
    "outputs": [],
    "source": [
-    "# YOUR CODE HERE\n",
-    "raise NotImplementedError()"
+    "# We assume the definitions of the previous block as not to copy everything.\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()"
    ]
   },
   {