Kinetic over-relaxation method for the convection equation with Fourier solver

In this paper, we apply the CFL-less kinetic over-relaxation scheme presented in [1] to the convection equation in two space dimensions. The method is a succession of free-transport steps and collisions steps. The free transport steps are solved with Fourier discretization. The collision steps are solved with over-relaxation for achieving high order The method reaches six-order accuracy when using palindromic composition method. We apply the method to the guiding-center model in plasma physics.