Instability of the filtering method for Vlasov's equation

摘要

Klimas has introduced a smoothed Fourier-Fourier method. This method consists in convolving the original distribution function with a Gaussian distribution function, and, next, in solving the new system with a transformed splitting algorithm. Unfortunately, a second-order term appears in the new equation. In this work, it is studied how this term affects the numerical equation. In particular it is proven that instability occurs in the linear version of the Vlasov equation obtained by considering only free non- interacting particles. It is proved that the use of Fourier-Fourier transform is a fundamental requirement to solve this new equation. An important property is pointed out concerning the filtered distribution function in the transformed space. (K.A.) 14 refs.