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
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 CALVI - Scientific computation and visualization
4 IRMA - Institut de Recherche Mathématique Avancée

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.

Domaines: Analyse numérique [math.NA]

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