Theory and numerical approximations for a nonlinear 1 + 1 Dirac system
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 4, p. 841-874

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.

DOI : https://doi.org/10.1051/m2an/2011071
Classification:  35L40,  35L50,  35Q41,  65M06,  65M12,  65M15,  81Q05
Keywords: 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {4},
     year = {2012},
     pages = {841-874},
     doi = {10.1051/m2an/2011071},
     zbl = {1274.65232},
     mrnumber = {2891472},
     language = {en},
     url = {http://www.numdam.org/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, Volume 46 (2012) no. 4, pp. 841-874. doi : 10.1051/m2an/2011071. http://www.numdam.org/item/M2AN_2012__46_4_841_0/

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