Numerical Solution of the Fokker-Planck Equation Using Orthogonal Collocation

Abstract

This study aims to propose a numerical methodology to solve the Fokker-Planck Equation using the Orthogonal Collocation Method. In this approach, the original problem, represented by a partial differential equation, is rewritten as a system of initial value equations via discretization of spatial variable. The resulting system is integrated considering the Runge-Kutta-Fehlberg Method. The proposed methodology is applied in three case studies that presented an analytical solution. The obtained results demonstrate that the proposed approach is a good alternative for solving this class of problems. Keywords: Fokker-Planck Equation, Orthogonal Collocation, Numerical Method.