A numerical solution to the Vlasov equation Original Research Article

A fast, accurate and robust method to obtain a numerical solution to the Vlasov equation is presented. The method is based on time splitting to separate the initial equation into a set of simple transport type equations, and the solution of the resulting split equations by a fluid flux balance method. The goal of the present paper is to present this method for constant coefficients, and to show its extension to second order in phase space variable for equations such as the relativistic or the gyrokynetic Vlasov equation. Numerical results of simulations in 1 and 2 dimensions are presented.