A Rosenau-type approach to the approximation of the linear Fokker--Planck equation

TL;DR

This paper introduces a novel Rosenau-type method for approximating the linear Fokker-Planck equation, inspired by heat equation approximation techniques, and extends it to higher-order linear diffusion equations.

Contribution

It proposes a new Rosenau-type approach for the Fokker-Planck equation and generalizes it to higher-order linear diffusion equations.

Findings

Provides a consistent approximation method for the Fokker-Planck equation.

Extends Rosenau's heat equation approximation to higher-order diffusion equations.

Offers a potentially more accurate numerical scheme for complex diffusion problems.

Abstract

{The numerical approximation of the solution of the Fokker--Planck equation is a challenging problem that has been extensively investigated starting from the pioneering paper of Chang and Cooper in 1970. We revisit this problem at the light of the approximation of the solution to the heat equation proposed by Rosenau in 1992. Further, by means of the same idea, we address the problem of a consistent approximation to higher-order linear diffusion equations.