Exponential DG methods for Vlasov equations.

In this work, an exponential Discontinuous Galerkin (DG) method is proposed to solve numerically Vlasov type equations. The DG method is used for space discretization which is combined exponential Lawson Runge-Kutta method for time discretization to get high order accuracy in time and space. In addition to get high order accuracy in time, the use of Lawson methods enables to overcome the stringent condition on the time step induced by the linear part of the system. Moreover, it can be proved that a discrete Poisson equation is preserved. Numerical results on Vlasov-Poisson and Vlasov Maxwell equations are presented to illustrate the good behavior of the exponential DG method. • The main novelty of the paper is the development of high order exponential DG method for Vlasov type equations. • It involves the calculation of exponential of DG-matrices on this topic. • A discrete Poisson equation in DG frame work is given and satisfied. • These methods allow to derive high order accuracy in time, space and velocity. • These methods still ensure stability without the restrictive CFL type constraint coming from the linear part. [ABSTRACT FROM AUTHOR]