Instability of the filtering method for Vlasov's equation (Q1976846)

The authors study the phase space filamentation of distribution function by using numerical methods for non-stationary Vlasov-Poisson system which are based on splitting schemes. The one-dimensional nonstationary problem is considered, and stability properties are investigated for Vlasov-Poisson system and for the equation for smoothed distribution function. It is shown that the solution of the equation for smoothed distribution function is very sensitive to perturbations. The authors also prove the stability of linear version of Vlasov equation when only free non-interacting particles are considered. In the present method, the possibility of the use of Fourier transform is the main requirement for solving Cauchy problem numerically.