A Finite Difference–Hybrid Block Framework for Efficient Solution of Fokker-Planck Problems

Document Type : Research Paper

Authors
Morteza Bisheh-Niasar 1
Higinio Ramos 2
Mehdi Sabzevari 1
1 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
2 Department of Applied Mathematics, Faculty of Sciences, University of Salamanca, 37008. Salamanca, Spain
10.22055/jacm.2025.48147.5012
Abstract
We present a new numerical method to solve linear and non-linear Fokker-Planck equations‎. ‎Our technique is based on a combination of finite differences and block hybrid methods‎. ‎First‎, ‎we discretize the Fokker-Planck equation in space through central finite differences, which yields a system of ordinary differential equations‎. ‎Then‎, ‎we employ a one-step hybrid block method with three optimized points to solve the resulting nonlinear system of ordinary differential equations‎. ‎The fundamental properties of the proposed block hybrid method have been investigated‎ ‎in order to address its convergence‎. ‎Numerical results validate the effectiveness of our proposed technique‎.
Keywords
Fokker-Planck equation
Hybrid block method
Zero-stability
Consistency
Subjects

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Journal of Applied and Computational Mechanics
Volume 12, Issue 2
Spring 2026
Pages 515-522