Szukana fraza: [Abstract = "We construct a numerical scheme based on semi\-Lagrangian methods and time splitting techniques. We develop a four\-dimensional phase space algorithm for the distribution function while the electromagnetic field is solved on a two\-dimensional Cartesian grid. Finally, we present two nontrivial test cases\: \(a\) the wave Landau damping and \(b\) the electromagnetic beam\-plasma instability. For these cases our numerical scheme works very well and is in agreement with analytic kinetic theory."]