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9 Stability Condition

The stability of the finite difference method is essential. The scheme in Equation 48 is explicit in time; for each new step the wave values are determined from the previous values. The mesh spacing is h. The size of the time step dt is limited; information cannot be propagated across the mesh faster than the mesh velocity. The mesh velocity is . Hence, the time step must be bounded, and for the difference equation this limit is

where is the number of spatial dimensions.