he schemes
(
Implicit
scheme
),(
Explicit
scheme
),(
Crank Nicolson
) take the following
forms:
where the
notation introduced earlier refers to the
direction.
We recall from the (
Laplace spectrum
)
that
Hence, according to the spectral mapping theorem
(
Spectral
mapping
)


(Implicit spectrum)



(Krank Nicolson spectrum)

In every case it is sufficient to
have
Hence, the explicit scheme
is stable if
or
The other two schemes are always stable.
