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

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 Delta t(2) + h(2) + h(2) /Delta t) for Verlet] are obtained, where Delta t and h = max(Delta x, Delta v) are the discretization parameters.