Next: 5.1.2 Lax Scheme
Up: 5.1 Initial Value Problems
Previous: 5.1 Initial Value Problems
5.1.1 FTCS Scheme; Stability Analysis
Writing
and using
DNGF for the time derivative (FT, ``forward-time''), and
DST for the space derivative (CS, for ``centered-space''), we write
as
Stability analysis (J. v. Neumann):
At time , expand :
where
. Insert this in
to find
each Fourier component's propagation law,
.
Stable if
.
Application to FTCS + advective equation with :
or
Obviously, for any ; the FTCS method is inherently unstable.
Next: 5.1.2 Lax Scheme
Up: 5.1 Initial Value Problems
Previous: 5.1 Initial Value Problems
Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001