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Numerical dispersion relation
- How close is \tilde\omega to \omega ?
- Can solve for an explicit formula for \tilde\omega
\tilde\omega = \frac{2}{\Delta t}
\sin^{-1}\left( C\sin\left(\frac{k\Delta x}{2}\right)\right)
- \omega = kc is the analytical dispersion relation
- \tilde\omega = \tilde\omega(k, c, \Delta x, \Delta t) is the
numerical dispersion relation
- Speed of waves: c=\omega/k , \tilde c = \tilde\omega/k
- The numerical wave component has a wrong, mesh-dependent speed
