In general, Particle In Cell (PIC) methods have proven to be a very efficient tool for the numerical simulation of charged particle systems. The main advantage of such methods is that they can adequately give very good results for the low order moments of primary interest in particle beam transport with a fairly small number of particles, and thus make it possible to follow a particle beam for a long time. However, in some cases one may be interested in more detailed collective wave phenomena, which may occur over shorter time scales. Then, the statistical noise inherent in the PIC method can make it difficult to get an accurate description of the phenomenon. A better option for such problems can be to use Vlasov solvers, which discretize the full phase space on a multi-dimensional grid. This procedure is intrinsically devoid of statistical noise and numerical errors are only associated with the discretization of the Vlasov equation on the phase-space grid.