ote that for any pair of operators
and
we can
write
Hence, the
scheme
is equivalent to the
CrankNicolson
after grouping some
order
terms. Therefore, if CrankNicolson approximates with second order then so
does the scheme (*).
Claim
The scheme
preserves stability.
To transform the scheme (*) into a calculation recipe observe
that
We
conclude
Hence, we replaced inversion of
with consecutive inversions
and
.
