Fifth-order finite-difference scheme for Fokker-Planck equations with drift-admitting jumps

TL;DR

This paper introduces an improved fifth-order finite-difference scheme for solving Fokker-Planck equations with drift-admitting jumps, enhancing accuracy for discontinuous drifts and verified through numerical experiments.

Contribution

The paper presents a novel fifth-order scheme that maintains high accuracy even with discontinuous drifts, improving upon previous second-order methods.

Findings

Achieves fifth-order convergence for equations with drift-admitting jumps.

Numerical experiments confirm the scheme's improved accuracy.

Outperforms previous second-order methods in handling discontinuities.

Abstract

Recently a useful finite-difference scheme was proposed in [Phys. Rev. E 98, 033302 (2018)] to solve Fokker-Planck equations with drift-admitting jumps. However, while the scheme is fifth order for the case with smooth drifts, it is only second order for the case with discontinuous drifts. To rectify this, we propose in this paper an improved scheme that achieves a fifth-order convergence rate for the case with drift-admitting jumps. Numerical experiments are also employed to verify the validity of the scheme.