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July  2008, 10(1): 239-263. doi: 10.3934/dcdsb.2008.10.239

A linearly implicit finite difference method for a Klein-Gordon-Schrödinger system modeling electron-ion plasma waves

Pavlos Xanthopoulos 1, and  Georgios E. Zouraris 2,

1. 

Max-Planck-Institut für Plasmaphysik, Teilinstitut Greifswald, Wendelsteinstrasse 1, D-17491 Greifswald, Germany
2. 

Department of Mathematics, University of Crete, GR-714 09 Heraklion, Crete, Greece

Received  January 2007 Revised  September 2007 Published  April 2008

An initial and Dirichlet boundary value-problem for a Klein– Gordon–Schrödinger-type system of equations is considered, which describes the nonlinear interaction between high frequency electron waves and low frequency ion plasma waves in a homogeneous magnetic field. To approximate the solution to the problem a linearly implicit finite difference method is proposed, the convergence of which is ensured by deriving a second order error estimate in a discrete energy norm that is stronger than the discrete maximum norm. The numerical implementation of the method gives a computational confirmation of its order of convergence and recovers known theoretical results for the behavior of the solution, while revealing additional nonlinear features.
Keywords: plasma physics, linearly implicit finite difference method, a priori error estimates..
Mathematics Subject Classification: Primary: 65M12, 65M15, 65M06; Secondary: 82D1.
Citation: Pavlos Xanthopoulos, Georgios E. Zouraris. A linearly implicit finite difference method for a Klein-Gordon-Schrödinger system modeling electron-ion plasma waves. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 239-263. doi: 10.3934/dcdsb.2008.10.239
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