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→The method: The infinitesimal change in x and y didn't appear in the equations! see Press 1992 Numerical Recipes in C p 855-856 |
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: <math>{u_{ij}^{n+1}-u_{ij}^n\over \Delta t} =
{1 \over 2*\Delta^2}\left(\delta_x^2+\delta_y^2\right)
\left(u_{ij}^{n+1}+u_{ij}^n\right)</math>
with:
: \Delta = \Delta x = \Delta y
where <math>\delta_p</math> is the central difference operator for the ''p''-coordinate. After performing a [[Von Neumann stability analysis|stability analysis]], it can be shown that this method will be stable for any <math>\Delta t</math>.
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