An exponential integrator for a highly oscillatory vlasov equation

Emmanuel Frénod; Sever A. Hirstoaga; Eric Sonnendrücker

doi:10.3934/dcdss.2015.8.169

Article Contents

2015, Volume 8, Issue 1: 169-183. Doi: 10.3934/dcdss.2015.8.169

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An exponential integrator for a highly oscillatory vlasov equation

1.
Université de Bretagne-Sud, UMR 6205, LMBA, F-56000 Vannes
2.
Inria Nancy-Grand Est, CALVI Project, & IRMA (UMR CNRS 7501), Université de Strasbourg, 7, rue René-Descartes, 67084, Strasbourg
3.
Max Planck Institute for Plasma Physics, EURATOM Association, Boltzmannstr. 2, 85748 Garching

Received: March 31, 2013

Revised: April 30, 2013

Published: January 2015

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Abstract

In the framework of a Particle-In-Cell scheme for some 1D Vlasov-Poisson system depending on a small parameter, we propose a time-stepping method which is numerically uniformly accurate when the parameter goes to zero. Based on an exponential time differencing approach, the scheme is able to use large time steps with respect to the typical size of the fast oscillations of the solution.

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Mathematics Subject Classification: Primary: 35Q83, 35J05, 65N75, 65L04, 37M05.

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