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.
@article{M2AN_2012__46_4_841_0,
author = {Bournaveas, Nikolaos and Zouraris, Georgios E.},
title = {Theory and numerical approximations for a nonlinear 1 + 1 Dirac system},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {46},
year = {2012},
pages = {841-874},
doi = {10.1051/m2an/2011071},
mrnumber = {2891472},
zbl = {1274.65232},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2012__46_4_841_0}
}
Bournaveas, Nikolaos; Zouraris, Georgios E. Theory and numerical approximations for a nonlinear 1 + 1 Dirac system. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 46 (2012) pp. 841-874. doi : 10.1051/m2an/2011071. http://gdmltest.u-ga.fr/item/M2AN_2012__46_4_841_0/
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