Analysis of difference schemes for the Fokker–Planck angular diffusion operator

Abstract

This paper is dedicated to the mathematical analysis of difference schemes for discretizing the angular diffusion operator present in the azimuth-independent Fokker-Planck equation. The study establishes sets of sufficient conditions to ensure that the schemes achieve convergence of order 2, and provides insights into the rationale behind certain widely recognized discrete ordinates methods. In the process, interesting properties regarding Gaussian nodes and weights, which until now have remained unnoticed by mathematicians, naturally emerge.