Study guide: Finite difference methods for wave motion

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Computing the error in wave velocity

Introduce $p=k\Delta x/2$
(the important dimensionless spatial discretization parameter)

$p$ measures no of mesh points in space per wave length in space

Study error in wave velocity through $\tilde c/c$ as function of $p$

$r(C, p) = \frac{\tilde c}{c} = \frac{1}{Cp}{\sin}^{-1}\left(C\sin p\right), \quad C\in (0,1],\ p\in (0,\pi/2]$