Computing absolute and essential spectra using continuation

Rademacher, Jens D.M., Sandstede, Bjorn and Scheel, Arnd (2007) Computing absolute and essential spectra using continuation Physica D, 229. pp. 166-183.

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Abstract

A continuation approach to the computation of essential and absolute spectra of differential operators on the real line is presented. The advantage of this approach, compared with direct eigenvalue computations for the discretized operator, are the efficient and accurate computation of selected parts of the spectrum (typically those near the imaginary axis) and the option to compute nonlinear travelling waves and selected eigenvalues or other stability indicators simultaneously in order to locate accurately the onset to instability. We also discuss the implementation and usage of this approach with the software package AUTO and provide example computations for the FitzHugh–Nagumo and the complex Ginzburg–Landau equation.

Item Type:	Article
Divisions :	Faculty of Engineering and Physical Sciences > Mathematics
Authors :	Authors Email ORCID Rademacher, Jens D.M. UNSPECIFIED UNSPECIFIED Sandstede, Bjorn b.sandstede@surrey.ac.uk UNSPECIFIED Scheel, Arnd UNSPECIFIED UNSPECIFIED
Date :	15 May 2007
Identification Number :	https://doi.org/10.1016/j.physd.2007.03.016
Additional Information :	This is an author-prepared version of an article published in Physica D, 229, 166-183. © 2007 Elsevier Inc. All rights reserved. Click here to access the published version.
Depositing User :	Mr Adam Field
Date Deposited :	27 May 2010 14:41
Last Modified :	23 Sep 2013 18:33
URI:	http://epubs.surrey.ac.uk/id/eprint/1460

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