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An exponential integrator for a highly oscillatory Vlasov equation

Emmanuel Frenod 1, 2 Sever Adrian Hirstoaga 3, 2 Eric Sonnendrücker 4
2 CALVI - Scientific computation and visualization
IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
3 TONUS - TOkamaks and NUmerical Simulations
IRMA - Institut de Recherche Mathématique Avancée, Inria Nancy - Grand Est
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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Emmanuel Frenod, Sever Adrian Hirstoaga, Eric Sonnendrücker. An exponential integrator for a highly oscillatory Vlasov equation. Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2015, 8 (1), pp.169-183. ⟨10.3934/dcdss.2015.8.169⟩. ⟨hal-00833479⟩

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