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

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  • 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.
    Mathematics Subject Classification: Primary: 65M12, 65M15, 65M06; Secondary: 82D10.


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