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

Abstract

Abstract: In this paper we present some classes of high-order semi-Lagran- gian 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 $ L^2$ norm with a rate of $\displaystyle \mathcal{O}\left(\Delta t^2 +h^{m+1}+ \frac{h^{m+1}}{\Delta t}\right),$ where $ m$ is the degree of the polynomial reconstruction, and $ \Delta t$ and $ h$ are respectively the time and the phase-space discretization parameters