Abstract—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.

Index Terms—WENO schemes, vlasov equation, time splitting method.

Yacine Benhadid is with the PAAET, Kuwait (email: y.benhadid@hotmail.com).

Cite: Yacine Benhadid, "WENO Schemes for the Resolution of the Two-Dimensional Vlasov-Poisson System," International Journal of Applied Physics and Mathematics  vol. 3, no. 2, pp. 106-110, 2013.