 Leapfrog advection scheme

ID: leapfrog-advection-scheme

Centered space and leapfrog time discretization of

u_{t} + c u_{x} = 0

gives

u_{j}^{n + 1} = u_{j}^{n - 1} - ν (u_{j + 1}^{n} - u_{j - 1}^{n}), ν = c Δ t /Δ x .

Its amplification polynomial is

G^{2} + 2 i ν sin θ G - 1

. The two roots have unit modulus for

∣ ν sin θ ∣ \leq 1

, but a repeated unit root at equality violates the uniform root condition.

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