WENO Schemes for the Resolution of the Two-Dimensional Vlasov-Poisson System

A numerical resolution of the two dimensional Vlasov-Poisson system is proposed. The time splitting method is used on the Vlasov equations to reduce the dimensions, then we apply the WENO (weighted essentially non-oscillatory) scheme based on the idea of Harten to solve our equation. We elaborate a transformation time-space to avoid the mixed problem and reducing the error. This algorithm is applied to the two dimensional Vlasov-Poisson system and an evolution of the density and the total energy is presented