Kees' assignment

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Model equation

\frac{\partial H}{\partial t} = - \frac{\partial}{\partial x}D(x) \frac{\partial H}{\partial x} + M

where

D(x) = C H^{n+2}\frac{\partial h} {\partial x} ^{n-1} \frac{\partial h}{\partial x},

and

C =

Model parameters

  • \frac{\partial b}{\partial x} = -0.1
  • M(x) = M_0 - x M_1 = 4 - 2e-4 x

Numerical tips

Use a staggered grid such that D(x_{j+1/2}), so

Failed to parse (Missing texvc executable; please see math/README to configure.): D(x_{j+1/2}) = \frac{1}{2} \left(H_j + H_{j+1}\right)^5 \left(\frac{h_{j+1} + h_j}{\Delta x}