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.
Mots-clés : existence, uniqueness, finite difference methods, error estimates
@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 },
pages = {841--874},
publisher = {EDP-Sciences},
volume = {46},
number = {4},
year = {2012},
doi = {10.1051/m2an/2011071},
mrnumber = {2891472},
zbl = {1274.65232},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2011071/}
}
TY - JOUR AU - Bournaveas, Nikolaos AU - Zouraris, Georgios E. TI - Theory and numerical approximations for a nonlinear 1 + 1 Dirac system JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 841 EP - 874 VL - 46 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2011071/ DO - 10.1051/m2an/2011071 LA - en ID - M2AN_2012__46_4_841_0 ER -
%0 Journal Article %A Bournaveas, Nikolaos %A Zouraris, Georgios E. %T Theory and numerical approximations for a nonlinear 1 + 1 Dirac system %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 841-874 %V 46 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2011071/ %R 10.1051/m2an/2011071 %G en %F 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 , Tome 46 (2012) no. 4, pp. 841-874. doi : 10.1051/m2an/2011071. http://www.numdam.org/articles/10.1051/m2an/2011071/
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