Numerische Mathematik

, Volume 118, Issue 2, pp 329–366 | Cite as

Analysis of a new class of forward semi-Lagrangian schemes for the 1D Vlasov Poisson equations

  • Thomas Respaud
  • Eric SonnendrückerEmail author


The Vlasov equation is a kinetic model describing the evolution of a plasma which is a globally neutral gas of charged particles. It is self-consistently coupled with Poisson’s equation, which rules the evolution of the electric field. In this paper, we introduce a new class of forward semi-Lagrangian schemes for the Vlasov–Poisson system based on a Cauchy Kovalevsky (CK) procedure for the numerical solution of the characteristic curves. Exact conservation properties of the first moments of the distribution function for the schemes are derived and a convergence study is performed that applies as well for the CK scheme as for a more classical Verlet scheme. A L 1 convergence of the schemes will be proved. Error estimates [in \({O\left(\Delta{t}^2+h^2 + \frac{h^2}{\Delta{t}}\right)}\) for Verlet] are obtained, where Δt and h = max(Δx, Δv) are the discretization parameters.

Mathematics Subject Classification (2000)

65M12 65M25 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.IRMAUniversité de Strasbourg and INRIA-Nancy-Grand Est, CALVI Project-TeamStrasbourgFrance

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