Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

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

Document Type : Original Article

Authors
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.
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
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Volume 2, Issue 4
Autumn 2025
Pages 225-233

  • Receive Date 05 November 2025
  • Revise Date 13 November 2025
  • Accept Date 29 November 2025
  • First Publish Date 29 November 2025
  • Publish Date 01 November 2025