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5.2.1 FTCS Scheme for Parabolic DE
In
,
replace
by DNGF and
by DDST formula:
``forward time-centered space'' algorithm,
Using
this is
Stability:
For the -dependent growth factor we find
,
which tells us that for stability the condition is
where is the characteristic time for the diffusion over a distance
(i.e. one lattice space).
The FTCS scheme is simple and stable, but inefficient.
EXERCISE:
Remember the thermal conduction problem we considered
earlier? If you haven't done it then, do it now, using
FTCS. Interpret the behavior of the solution for varying time step
sizes in the light of the above stability considerations.
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Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001