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Numerical wave propagation (2)

The complete scheme, \lbrack D_tD_t e^{ikx}e^{-i\tilde\omega t} = c^2D_xD_x e^{ikx}e^{-i\tilde\omega t}\rbrack^n_q

leads to an equation for \tilde\omega : \sin^2\left(\frac{\tilde\omega\Delta t}{2}\right) = C^2\sin^2\left(\frac{k\Delta x}{2}\right), where C = \frac{c\Delta t}{\Delta x} is the Courant number

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