Matthies, K., 2003. Backward error analysis of a full discretization scheme for a class of semilinear parabolic partial differential equations. Nonlinear Analysis: Theory Methods & Applications, 52 (3), pp. 805-826.
A numerical method for reaction–diffusion equations with analytic nonlinearity is presented, for which a rigorous backward error analysis is possible. We construct a modified 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 first 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.
|Item Type ||Articles|
|Departments||Faculty of Science > Mathematical Sciences|
|Publisher Statement||backward.pdf: NOTICE: this is the author’s version of a work that was accepted for publication in Nonlinear Analysis: Theory, Methods & Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nonlinear Analysis: Theory, Methods & Applications, vol 52, issue 3, 2003, DOI 10.1016/S0362-546X(02)00134-7|
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