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

##### Abstract:

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.

##### Keywords:

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

##### References:

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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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