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.

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 : 10.1051/m2an/2011071
Classification : 35L40, 35L50, 35Q41, 65M06, 65M12, 65M15, 81Q05
Mots clés : existence, uniqueness, finite difference methods, error estimates
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     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},
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     zbl = {1274.65232},
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     url = {http://www.numdam.org/articles/10.1051/m2an/2011071/}
}
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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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