10: Draft task 1

Week 6/10 Hyperbolic PDEs.ipynb

@@ -39,7 +39,7 @@
    "cell_type": "raw",
    "metadata": {},
    "source": [
-    "team_members = \"\""
+    "team_members = \"Koen Vendrig, Kees van Kempen\""
    ]
   },
   {
@@ -66,7 +66,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -83,10 +83,7 @@
    },
    "outputs": [],
    "source": [
-    "# Import packages here ...\n",
+    "import numpy as np"
-    "\n",
-    "# YOUR CODE HERE\n",
-    "raise NotImplementedError()"
    ]
   },
   {
@@ -183,8 +180,31 @@
    "outputs": [],
    "source": [
     "def pdeHyperbolic(a, x, t, f, g):\n",
-    "    # YOUR CODE HERE\n",
+    "    # TODO: Docstring.\n",
-    "    raise NotImplementedError()"
+    "    \n",
+    "    n = len(t)\n",
+    "    m = len(x)\n",
+    "    \n",
+    "    # TODO: The stepsize is defined by fixed h (k), but the input x (t)\n",
+    "    #       could allow variable step size. What should it be?\n",
+    "    #h = x[1] - x[0]\n",
+    "    l = x[-1]\n",
+    "    h = l/(m - 1)\n",
+    "    k = t[1] - t[0]\n",
+    "    λ = a*k/h\n",
+    "    \n",
+    "    A = np.eye(m - 2)*2*(1 - λ**2) + ( np.eye(m - 2, m - 2, 1) + np.eye(m - 2, m - 2, -1) )*λ**2\n",
+    "    \n",
+    "    w = np.zeros((n, m))\n",
+    "    \n",
+    "    # Set initial values w[i, 0] = f[x[i]] and w[i, 1] = ...\n",
+    "    # TODO: Fix previous comment.\n",
+    "    w[:, 0] = f(x)\n",
+    "    # TODO: What does the length of x[1:]?\n",
+    "    w[:, 1] = (1 - λ**2)*f[x[1:m - 1]] + λ**2/2*f(x[2:m]) - λ**2/2*f(x[2:m]) + k*g(x[1:m - 1])\n",
+    "    \n",
+    "    for j in range(2, n):\n",
+    "        w[:, j] = "
    ]
   },
   {
@@ -441,7 +461,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
+   "display_name": "Python 3",
    "language": "python",
    "name": "python3"
   },