Original Research Article

Article volume = 2022 and issue = 1

Pages: 1–6

Article publication Date: November 21, 2022

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Numerical solutions of Fokker-Planck Equation based on Hermite functions

Manoochehr Khasi(a) and Fereshteh Samadi(b)

(a) Iran University of Science and Technology, Tehran, Iran.

(b) Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, Iran


In this research study, a spectral method based on Hermite functions is considered to solve the Fokker--Planck equation which is an equation governed by the time evolution of probability density function of the stochastic processes. Spatially the equation is discretized using a Galerkin method based on Hermite functions and the system of a first--order ordinary differential equation is obtained. Using an eigenvalue decomposition technique, the equation is transformed into a set of independent ordinary differential equations that can be solved analytically. Some numerical examples are included to show the accuracy and efficiency of the proposed approach.


Fokker-Planck equation, Hermite functions, spectral Galerkin method.

  • [1] Johnson Fok, Benyu Guo, and Tao Tang. Combined hermite spectral-finite difference method for the fokker-planck equation. Mathematics of computation, 71(240):1497–1528, 2002. 1
  • [2] Ben-yu Guo and Tian-jun Wang. Composite generalized laguerre-legendre spectral method with domain decomposition and its application to fokker-planck equation in an infinite channel. Mathematics of Computation, 78(265):129–151, 2009. 1
  • [3] Jing Guo, Cheng Wang, Steven M Wise, and Xingye Yue. An h2 convergence of a second-order convex-splitting, finitedifference scheme for the three-dimensional cahn–hilliard equation. Communications in Mathematical Sciences, 14(2):489–515, 2016. 1
  • [4] Hannes Risken. Fokker-planck equation. Springer, 1996. 1
  • [5] Jie Shen, Tao Tang, and Li-Lian Wang. Spectral methods: algorithms, analysis and applications, volume 41. Springer Science & Business Media, 2011. 2
Cite this article as:
  • Manoochehr Khasi and Fereshteh Samadi, Numerical solutions of Fokker-Planck Equation based on Hermite functions, Communications in Combinatorics, Cryptography & Computer Science, 2022(1), PP.1–6, 2022
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