A splitting operator-based finite difference method for the solution of 2D Fokker-Planck equations

Neena, A. S.; Clemence-Mkhope, Dominic P.; Awasthi, Ashish

doi:10.30511/ttmp.2025.2076836.1067

A splitting operator-based finite difference method for the solution of 2D Fokker-Planck equations

Document Type : Original Article

Authors

A. S. Neena ¹

Dominic P. Clemence-Mkhope ²

Ashish Awasthi ³

¹ National Institute of Technology Calicut

² North Carolina A & T State University, Greensboro, USA

³ Department of Mathematics, National Institute of Technology Calicut, Calicut-673601, Kerala, India.

10.30511/ttmp.2025.2076836.1067

Abstract

A simple and reliable numerical approach is constructed to solve the linear and nonlinear two-dimensional Fokker-Planck equations (FPEs). Initially, the Fokker–Planck equation is reformulated by decomposing it into one-dimensional components in the x and y directions. Then, local one-dimensional sub-equations are numerically solved by the explicit and implicit finite difference methods. The convergence of the proposed schemes is proved through truncation error and von Neumann stability analyses. The effectiveness and precision of the developed numerical methods are demonstrated using test problems, and the obtained outcomes are compared against the corresponding exact solutions for validation.

Keywords

Splitting operator

2D Fokker-Planck equation

Explicit finite difference scheme

Implicit finite difference scheme

von-Neumann stability

Subjects