Analysis of a new class of Forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson Equations

Details Analysis of a new class of Forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson Equations Analysis of a new class of Forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson Equations

2009-12-25

arxiv.org/abs/0912.4952v2

Mathematics

Numerical Analysis

Scientific paper

10.1007/s00211-010-0351-2

The Vlasov equation is a kinetic model describing the evolution of charged particles, and is coupled with Poisson's equation, which rules the evolution of the self-consistent 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. The convergence in L1 norm of the schemes is proved and error estimates are obtained.

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