Numerical Analysis of the Isotropic Fokker–Planck–Landau Equation

The homogeneous Fokker–Planck–Landau equation is investigated for Coulombic potential and isotropic distribution function, i.e., when the distribution function depends only on time and on the modulus of the velocity. We derive a conservative and entropy decaying semidiscretized Landau equation for which we prove the existence of global in-time positive solutions. This scheme is not based on the so-called “Landau–Log” formulation of the operator and ensures the physically relevant long-time behavior of the solution.