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Theory and numerical approximations for a nonlinear 1 + 1 Dirac system

Published online by Cambridge University Press:  03 February 2012

Nikolaos Bournaveas and
Georgios E. Zouraris
Nikolaos Bournaveas
Affiliation:
Department of Mathematics, University of Edinburgh, JCMB, King’s Buildings, Edinburgh, EH9 3JZ, Scotland, UK. N.Bournaveas@ed.ac.uk
Georgios E. Zouraris
Affiliation:
Department of Mathematics, University of Crete, 714 09 Heraklion, Crete, Greece; zouraris@math.uoc.gr

Abstract

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We consider a nonlinear Dirac system in one space dimension with periodic boundary conditions. First, we discuss questions on the existence and uniqueness of the solution. Then, we propose an implicit-explicit finite difference method for its approximation, proving optimal order a priori error estimates in various discrete norms and showing results from numerical experiments.

Keywords

Existenceuniquenessfinite difference methodserror estimates

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 4 , July 2012, pp. 841 - 874
Copyright
© EDP Sciences, SMAI, 2012

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