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High order Runge-Kutta-Nyström splitting methods for the Vlasov-Poisson equation

Nicolas Crouseilles 1, 2 Erwan Faou 1, 2 Michel Mehrenberger 3, 4
1 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
3 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
Abstract : In this work, we derive the order conditions for fourth order time splitting schemes in the case of the $1D$ Vlasov-Poisson system. Computations to obtain such conditions are motivated by the specific Poisson structure of the Vlasov-Poisson system : this structure is similar to Runge-Kutta-Nyström systems. The obtained conditions are proved to be the same as RKN conditions derived for ODE up to the fourth order. Numerical results are performed and show the benefit of using high order splitting schemes in that context.
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https://hal.inria.fr/inria-00633934
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Submitted on : Wednesday, October 19, 2011 - 7:23:22 PM
Last modification on : Friday, June 19, 2020 - 9:22:04 AM
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  • HAL Id : inria-00633934, version 1

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Nicolas Crouseilles, Erwan Faou, Michel Mehrenberger. High order Runge-Kutta-Nyström splitting methods for the Vlasov-Poisson equation. 2011. ⟨inria-00633934⟩

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