Enhanced fifth-kind Chebyshev polynomial Petrov–Galerkin algorithm for time-fractional Fokker–Planck equation

E. Magdy (), A. G. Atta (), G. M. Moatimid (), W. M. Abd-Elhameed and Y. H. Youssri
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E. Magdy: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
A. G. Atta: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
G. M. Moatimid: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
W. M. Abd-Elhameed: �Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah, Saudi Arabia¶Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
Y. H. Youssri: �Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 12, 1-22

Abstract: This paper employs a numerical method for the numerical treatment of the time fractional Fokker–Planck equation. This method is based on applying the spectral Petrov–Galerkin method. We utilize suitable combinations for the shifted Chebyshev polynomial of the fifth-kind as basis functions. The key idea of the suggested strategy is to transform the governed boundary-value problem into a set of linear algebraic equations using the spectral Petrov–Galerkin method. Several approaches are available to solve the resultant linear system. An in-depth investigation is conducted on the convergence and error analysis of the expansion of the shifted Chebyshev polynomial function of the fifth kind. Many examples are provided to illustrate the precision of the suggested approach.

Keywords: Fractional Fokker–Planck equation; Chebyshev polynomials; spectral methods; convergence analysis (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0129183124501626

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