 Leapfrog finite-difference scheme for the diffusion equation

ID: leapfrog-finite-difference-scheme-for-the-diffusion-equation

Applying a centered leapfrog step in time and the centered second difference in space to

u_{t} = u_{xx}

gives

u_{m}^{n + 1} = u_{m}^{n - 1} + 2 μ (u_{m - 1}^{n} - 2 u_{m}^{n} + u_{m + 1}^{n}) .

For every

μ > 0

, each nonconstant Fourier mode has an amplification root of modulus greater than one, so the scheme is unconditionally unstable.

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