Conservative and Entropy Decaying Numerical Scheme for the Isotropic Fokker–Planck–Landau Equation

Abstract

Homogeneous Fokker–Planck–Landau equation denoted by FPLE is studied for Coulombian and isotropic distribution function, i.e. when the distribution function depends only on time and on the modulus of the velocity. We derive a new conservative and entropy decaying semi-discretized FPLE for which we prove the existence of global in time, positive. For the time-discretized equation, we give upper bound for the time step which guarantes positivity and entropy decay of the numerical solution.