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Journal of Scientific Computing

Erschienen in:

01.06.2015

Computing Interacting Multi-fronts in One Dimensional Real Ginzburg Landau Equations

verfasst von: Tasos Rossides, David J. B. Lloyd, Sergey Zelik

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2015

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Abstract

We develop an efficient and robust numerical scheme to compute multi-fronts in one-dimensional real Ginzburg–Landau equations that range from well-separated to strongly interacting and colliding. The scheme is based on the global centre-manifold reduction where one considers an initial sum of fronts plus a remainder function (not necessarily small) and applying a suitable projection based on the neutral eigenmodes of each front. Such a scheme efficiently captures the weakly interacting tails of the fronts. Furthermore, as the fronts become strongly interacting, we show how they may be added to the remainder function to accurately compute through collisions. We then present results of our numerical scheme applied to various real Ginzburg Landau equations where we observe colliding fronts, travelling fronts and fronts converging to bound states. Finally, we discuss how this numerical scheme can be extended to general PDE systems and other multi-localised structures.

Vorheriger Artikel Contraction and Optimality Properties of an Adaptive Legendre–Galerkin Method: The Multi-Dimensional Case

Nächster Artikel Dynamic Model Adaptation for Multiscale Simulation of Hyperbolic Systems with Relaxation

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Throughout this paper we will use the terms front and kink interchangeably and similarly for back and anti-kink.

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Titel: Computing Interacting Multi-fronts in One Dimensional Real Ginzburg Landau Equations
verfasst von: Tasos Rossides
David J. B. Lloyd
Sergey Zelik
Publikationsdatum: 01.06.2015
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2015
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-014-9917-y

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