Numerical Solution of Fokker-Planck-Kolmogorov Time Fractional Differential Equations Using Haar Wavelet Method and convergence and error analysis

Subject Areas : Numerical Analysis

Shaban Mohammadi ¹ , Seyed Reza Hejazi ²

1 - Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran.
2 - Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran.

Received: 2021-10-31 Accepted : 2022-08-16 Published : 2022-06-01

Keywords: Haar wavelet, Time fractional differential equations, Fokker-Planck-Kolmogorov differential equations,

Abstract :

The purpose of this paper is to present an efficient numerical method for finding numerical solutions Fokker-Planck-Kolmogorov time-fractional differential equations. The Haar Wave was the first to be introduced. The Fokker-Planck-Kolmogorov time-fractional differential equation is converted to the linear equation using the Haar wavelet operation matrix in this technique. This method has the advantage of being simple to solve. The simulation was carried out using MATLAB software. Finally, the proposed strategy was used to solve certain problems. The results revealed that the suggested numerical method is highly accurate and effective when used to Fokker-Planck-Kolmogorov time fraction differential equations. The results for some numerical examples are documented in table and graph form to elaborate on the efficiency and precision of the suggested method. Moreover, for the convergence of the proposed technique, inequality is derived in the context of error analysis.

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