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

Nikolaos Bournaveas; Georgios E. Zouraris

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 4, page 841-874
  • ISSN: 0764-583X

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.

How to cite

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Bournaveas, Nikolaos, and Zouraris, Georgios E.. "Theory and numerical approximations for a nonlinear 1 + 1 Dirac system." ESAIM: Mathematical Modelling and Numerical Analysis 46.4 (2012): 841-874. <http://eudml.org/doc/276381>.

@article{Bournaveas2012,
abstract = {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.},
author = {Bournaveas, Nikolaos, Zouraris, Georgios E.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Existence; uniqueness; finite difference methods; error estimates; implicit-explicit finite difference method; nonlinear Dirac system},
language = {eng},
month = {2},
number = {4},
pages = {841-874},
publisher = {EDP Sciences},
title = {Theory and numerical approximations for a nonlinear 1 + 1 Dirac system},
url = {http://eudml.org/doc/276381},
volume = {46},
year = {2012},
}

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
DA - 2012/2//
PB - EDP Sciences
VL - 46
IS - 4
SP - 841
EP - 874
AB - 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.
LA - eng
KW - Existence; uniqueness; finite difference methods; error estimates; implicit-explicit finite difference method; nonlinear Dirac system
UR - http://eudml.org/doc/276381
ER -

References

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