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.