From 950b0a015a3a345e3c3bb10a7d349e5e31d165f6 Mon Sep 17 00:00:00 2001 From: Kees van Kempen Date: Tue, 15 Mar 2022 10:46:16 +0100 Subject: [PATCH] 10: Docstring --- Week 6/10 Hyperbolic PDEs.ipynb | 49 ++++++++++++++++++++++++--------- 1 file changed, 36 insertions(+), 13 deletions(-) diff --git a/Week 6/10 Hyperbolic PDEs.ipynb b/Week 6/10 Hyperbolic PDEs.ipynb index 18c5b09..83fa6f0 100644 --- a/Week 6/10 Hyperbolic PDEs.ipynb +++ b/Week 6/10 Hyperbolic PDEs.ipynb @@ -66,7 +66,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 1, "metadata": { "deletable": false, "nbgrader": { @@ -163,7 +163,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 2, "metadata": { "deletable": false, "nbgrader": { @@ -181,7 +181,24 @@ "outputs": [], "source": [ "def pdeHyperbolic(a, x, t, f, g):\n", - " # TODO: Docstring.\n", + " \"\"\"\n", + " Numerically solves the hyperbolic differential equation ∂^2u(x,t)/∂t^2 - a*∂^2u(x,t)/∂x^2 = 0\n", + " with constant a for boundary conditions given by\n", + " u(0, t) = 0 = u(x[-1], t) for all t\n", + " y(x, 0) = f(x)\n", + " ∂u(x, t)/∂t = g(x) for t = 0 and all x\n", + "\n", + " Args:\n", + " a: numerical constant in the PDE\n", + " x: array of evenly spaced space values x in the PDE\n", + " t: array of evenly spaced times values t in the PDE\n", + " f: callable function of numerical x giving a boundary condition to solution u of the PDE\n", + " g: callable function of numerical x giving a boundary condition to derivative ∂u/∂t of the PDE\n", + "\n", + " Returns:\n", + " An |t| by |x| matrix w giving approximate solutions to the PDE over the grid\n", + " imposed by arrays x and t, such that w[j, i] corresponds to u[x[i], y[j]].\n", + " \"\"\"\n", " \n", " n = len(t)\n", " m = len(x)\n", @@ -194,14 +211,17 @@ " k = t[1] - t[0]\n", " λ = a*k/h\n", " \n", + " # Create the tri-diagonal matrix A of size (m - 2) by (m - 2).\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", + " # Create empty matrix w for the result.\n", " w = np.zeros((n, m))\n", " \n", - " # Set initial values for w[i, 0] and w[i, 1]\n", + " # Set initial values for w[0, i] and w[1, i].\n", " w[0] = f(x)\n", - " w[1, 1:m - 1] = (1 - λ**2)*f(x[1:m - 1]) + λ**2/2*f(x[2:m]) - λ**2/2*f(x[0:m - 2]) + k*g(x[1:m - 1])\n", + " w[1, 1:m - 1] = (1 - λ**2)*f(x[1:m - 1]) + λ**2/2*f(x[2:m]) + λ**2/2*f(x[0:m - 2]) + k*g(x[1:m - 1])\n", " \n", + " # Loop over all times t[j] to find w[j, i].\n", " for j in range(2, n):\n", " w[j, 1:m - 1] = np.dot(A, w[j, 1:m - 1]) - w[j - 1, 1:m - 1]\n", " \n", @@ -252,7 +272,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 3, "metadata": { "deletable": false, "nbgrader": { @@ -272,22 +292,22 @@ "name": "stdout", "output_type": "stream", "text": [ - "0.9999862004036565\n" + "1.020779125224177\n" ] }, { "data": { "text/plain": [ - "[]" + "[]" ] }, - "execution_count": 39, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": "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\n", + "image/png": "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\n", "text/plain": [ "
" ] @@ -299,7 +319,7 @@ } ], "source": [ - "# There is an 𝑙 in the boundary conditions we assume should be a 1. (-1 pt)\n", + "# There is an 𝑙 in the boundary conditions we assume should be a 1. (-1 pts)\n", "a = 1\n", "x = np.linspace(0, 1, 300)\n", "t = np.linspace(0, 1, 300)\n", @@ -319,8 +339,11 @@ "jlist = np.arange(1, 300)\n", "ilist = np.arange(1, 300)\n", "\n", - "plt.plot(t[jlist], u(x[ilist], t[jlist]))\n", - "plt.plot(t[jlist], w[jlist, ilist])" + "#plt.plot(t[jlist], u(x[ilist], t[jlist]))\n", + "#plt.plot(t[jlist], w[jlist, ilist])\n", + "\n", + "plt.plot(t, u(x, t))\n", + "plt.plot(t, w[np.arange(300), np.arange(300)])" ] }, {