Fast spectral methods for the Fokker-Planck-Landau collision operator

In this paper we present a new spectral method for the fast evaluation of t he Fokker-Planck-Landau (FPL) collision operator. The method allows us to o btain spectrally accurate numerical solutions with simply O (n lag(2) n) op erations in contrast with the usual O (n(2)) cost of a deterministic scheme . We show that the method preserves the total mass whereas momentum and ene rgy are approximated with spectral accuracy. Numerical results for the mi, equation for Maxwell molecules and for Coulomb interactions in two and thre e dimensions in velocity space are also given. (C) 2000 Academic Press.