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.
