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In order to satisfy (5.10), with defined by (5.6) we set
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).