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 
. The size of the time step 
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.
In two dimensions the stability condition is
The maximum time step size is bounded by
