Now, we have, recalling (5.7) and (5.8),

and in order to satisfy (5.9), we set

We have written here , where is either of or . In this case, will be positive if

and we have an upper bound on the time step in terms of the grid spacing. In the constant-coefficient case, we note that this is the same requirement as for the stability of scheme (5.3).

Stefan Bilbao 2002-01-22