The leapfrog scheme applied to the equation: $$\frac{dz}{dt} = \lambda z$$ gives $$\frac{z^{n+1} - z^{n-1}}{2\Delta t} = \lambda z^n.$$ The region of absolute stability is calculated and it is the pure imaginary interval $-i\leq \lambda \Delta t\leq i$. From that how can I conclude that what are the stability restrictions of the leapfrog scheme applied to the diffusion equation with periodic boundary conditions?
2026-03-28 15:26:17.1774711577
Stabilty of leapfrog scheme applied to wave equation
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