Fourier-Fourier numerical method for Vlasov-Poisson system and comparison of different Fourier filters for suppression of the filamentation in the velocity space.

We compare numerical methods (Fourier-Fourier method with various Fourier filters in the velocity space vs. finite difference and finite volume methods) for evolution of nonlinear periodic Langmuir waves via solving 1D+1V Vlasov-Poisson system. The focus is made on the solution accuracy during a long term evolution for which some kind of numerical filtering in velocity space is inevitable due to increasing filamentation issue in the velocity space (formation of the sharp features in the solution) and impossibility of resolving such solutions accurately in the long run. Explicit filters are used for Fourier-Fourier method while similar effects come in implicitly for finite difference and finite volume methods due to their discretizations.