A numerical solution to the Vlasov equation

A fast, accurate and robust method to obtain a numerical solution to the Vl asov equation is presented. The method is based on lime splitting to separa te the initial equation into a set of simple transport type equations, and the solution of the resulting split equations by a fluid flux balance metho d. The goal of the present paper is to present this method for constant coe fficients, and to show its extension to second order in phase space variabl e for equations such as the relativistic or the gyrokynetic Vlasov equation . Numerical results of simulations in 1 and 2 dimensions are presented. (C) 1999 Elsevier Science B.V.