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MCS
2008
Springer

Validated continuation over large parameter ranges for equilibria of PDEs

8 years 2 months ago
Validated continuation over large parameter ranges for equilibria of PDEs
Validated continuation was introduced in [4] as means of checking that the classical continuation method applied to a Galerkin projection of a PDE provides a locally unique equilibrium to the PDE of interest. In this paper we extend the numerical technique to include a parameter that leads to better bounds on the errors associated with the Galerkin truncation. We test this method on the Swift-Hohenberg and Cahn-Hilliard equations on one dimensional domains. For the first equation, we find no numerical obstructions to the validated continuation technique. This is not the case for the Cahn-Hilliard equation.
Marcio Gameiro, Jean-Philippe Lessard, Konstantin
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2008
Where MCS
Authors Marcio Gameiro, Jean-Philippe Lessard, Konstantin Mischaikow
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