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

Pavlos Xanthopoulos; Georgios E. Zouraris

doi:10.3934/dcdsb.2008.10.239

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2008, Volume 10, Issue 1: 239-263. Doi: 10.3934/dcdsb.2008.10.239

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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
2.
Department of Mathematics, University of Crete, GR-714 09 Heraklion, Crete

Received: December 31, 2006

Revised: August 31, 2007

Published: December 2007

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Abstract

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: 82D10.

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