Theory and numerical approximations for a nonlinear 1 + 1 Dirac system
1 Department of Mathematics, University of Edinburgh, JCMB, King’s Buildings, Edinburgh, EH9 3JZ, Scotland, UK
2 Department of Mathematics, University of Crete, 714 09 Heraklion, Crete, Greece
Received: 18 March 2011
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.
Mathematics Subject Classification: 35L40 / 35L50 / 35Q41 / 65M06 / 65M12 / 65M15 / 81Q05
Key words: Existence / uniqueness / finite difference methods / error estimates
© EDP Sciences, SMAI, 2012