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.

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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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