Validated continuation over large parameter ranges for equilibria of PDEs

Marcio Gameiro, Jean-Philippe Lessard and Konstantin Mischaikow

Mathematics and Computers in Simulation (MATCOM), 2008, vol. 79, issue 4, 1368-1382

Abstract: Validated continuation was introduced [S. Day, J.-P. Lessard, K. Mischaikow, Validated continuation for equilibria of PDEs, SIAM Journal on Numerical Analysis, in press] 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 Allen–Cahn 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 Allen–Cahn equation.

Keywords: Equilibria; Validated continuation; PDE; Rigorous numerics (search for similar items in EconPapers)
Date: 2008
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475408001419
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2008:i:4:p:1368-1382

DOI: 10.1016/j.matcom.2008.03.014

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().