Convergence of classes of high-order semi-Lagrangian schemes for the Vlasov-Poisson system

In this paper we present some classes of high-order semi-Lagrangian schemes for solving the periodic one-dimensional Vlasov-Poisson system in phase-space on uniform grids. We prove that the distribution function f(t, x, v) and the electric field E(t, x) converge in the L2 norm with a rate of O ( ∆t + h + hm+1 ∆t ) , where m is the degree of the polynomial reconstruction, and ∆t and h are respectively the time and the phase-space discretization parameters.