The semi-Lagrangian method for the numerical resolution of the Vlasov equation

The numerical resolution of kinetic equations and, in particular, of Vlasov -type equations is performed most of the time using particle in cell method s which consist in describing the time evolution of the equation through a finite number of particles which follow the characteristic curves of the eq uation, the interaction with the external and self-consistent fields being resolved using a grid. Another approach consists in computing directly the distribution function on a grid by following the characteristics backward i n time for one time step and interpolating the Value at the feet of the cha racteristics using the grid point values of the distribution function at th e previous time step. In this report we introduce this last method, which c ouples the Lagrangian and Eulerian points of view and its use for the Vlaso v equation and equations derived from it. (C) 1999 Academic Press.