Finite difference approximations of the spatially homogeneous Fokker–Planck–Landau equation

Abstract

Finite difference methods are developed for approximating the spatially homogeneous Fokker–Planck–Landau equation for Coulomb collisions. The numerical methods apply the Fast Fourier Transform to improve time efficiency. Computational work is then done to compare the numerical approximations using FFT with the numerical method of Wollman (2017). In addition, some computations are done to verify the theoretical rate of convergence of the FPL equation proved in Strain and Guo (2008).