M1 Mathematics, 2011-2012
MM26E Numerical Approximation of PDEs
Hervé Le Dret
The finite difference method for the heat equation
The leapfrog scheme
Below is an animation showing a computation of the heat equation solution using the leapfrog scheme. The scheme is always unstable and diverges violently as can be seen on this example. Notice the scale of the plot toward the end.
The animation shows the numerical solution up to time $T=1$. It then loops back at $t=0$. Computations performed with Scilab.
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