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Backward error analysis of a full discretization scheme for a class of semilinear parabolic partial differential equations

✍ Scribed by Karsten Matthies

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
190 KB
Volume
52
Category
Article
ISSN
0362-546X

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✦ Synopsis

A numerical method for reaction-di usion equations with analytic nonlinearity is presented, for which a rigorous backward error analysis is possible. We construct a modiΓΏed equation, which describes the behavior of the full discretization scheme up to exponentially small errors in the step size. In the construction the numerical scheme is ΓΏrst exactly embedded into a nonautonomous equation. This equation is then averaged with only exponentially small remainder terms. The long-time behavior near hyperbolic equilibria, the persistence of homoclinic orbits and regularity properties are analyzed.

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