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5.1.2 Lax Scheme
Replacing in the FTCS formula the term
by its spatial
average
, we approximate
by
Stability / Friedrichs-Löwy condition:
Insert Fourier expanded in Lax formula to find
The condition is tantamount to
Region below the dashed line: physically relevant for ,
according to
Close scrutiny shows that LAX solves not the original PDE but
The additional diffusive term makes the method stable.
However, it is an artefact and should be small:
Next: 5.1.3 Leapfrog Scheme (LF)
Up: 5.1 Initial Value Problems
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Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001