Eulerian codes for the numerical solution of the Vlasov equation

A historical overview of Eulerian codes for the numerical solution of the Vlasov equation is presented, with special attention to characteristic methods. An evaluation of the performance of the cubic spline used for interpolation in the characteristic methods, with respect to other methods of interpolation, will be presented by comparing the solutions obtained by solving numerically different Vlasov–Poisson and Vlasov–Maxwell systems on a fixed Eulerian grid. Some recent developments of characteristic methods in two dimensions will be presented.