5.1.3 Leapfrog Scheme (LF)

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5.1.3 Leapfrog Scheme (LF)

Use DST for $\partial/\partial t$ : $\partial u /\partial t \approx (u^{n+1}-u^{n-1})/2\Delta t$ to find the leapfrog expression

$\displaystyle \fbox{$ \displaystyle \mbox{$\bf u$}_{j}^{n+1}-\mbox{$\bf u$}_{j}... ...\Delta x} \left[\, \mbox{$\bf j$}_{j+1}^{n}-\mbox{$\bf j$}_{j-1}^{n} \right] $}$

$\begin{figure}\includegraphics[width=120pt]{figures/f5lf.ps} \end{figure}$

Stability requires once more that $c\,\Delta t/\Delta x \leq 1$ (CFL condition)

Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001