diff --git a/Week 6/10 Hyperbolic PDEs.ipynb b/Week 6/10 Hyperbolic PDEs.ipynb index 7559a98..4e65dfc 100644 --- a/Week 6/10 Hyperbolic PDEs.ipynb +++ b/Week 6/10 Hyperbolic PDEs.ipynb @@ -387,7 +387,17 @@ "outputs": [], "source": [ "def test_pdeHyperbolic():\n", - " # TODO: Docstring\n", + " \"\"\"\n", + " Check that function pdeHyperbolic returns solutions for the PDE\n", + " ∂^2/∂𝑡^2 𝑢(𝑥,𝑡) − ∂^2/∂𝑥^2 𝑢(𝑥,𝑡) = 0 for boundary conditions given by\n", + " 𝑢(0, t) = 0 = 𝑢(x[-1], t) for all 0 <= t <= 1\n", + " y(x, 0) = f(x) for all 0 <= x <= 1\n", + " ∂𝑢(x, t)/∂t = g(x) for t = 0 and all 0 <= x <= 1\n", + " that are within tolerance (TOL = 1e-5) of the exact solution\n", + " 𝑢(𝑥,𝑡) = sin(2𝜋𝑥)(cos(2𝜋𝑡)+sin(2𝜋𝑡)),\n", + " using a grid of x and t values of each 1200 equidistant points.\n", + " \"\"\"\n", + " \n", " a = 1\n", " l = 1\n", " x = np.linspace(0, l, 1200)\n",