Jacobi Rational Operational Approach for Time-Fractional Sub-Diffusion Equation on a Semi-Infinite Domain

Authors

  • R. M. Hafez Department of Mathematics, Faculty of Education, Matrouh University, Matrouh 51744, Egypt
  • Y. H. Youssri Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt https://orcid.org/0000-0003-0403-8797
  • A. G. Atta Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt

DOI:

https://doi.org/10.37256/cm.4420233594

Keywords:

collocation method, Jacobi Rational (JR) Polynomials, Operational Matrix (OM), sub-diffusion equation

Abstract

In this study, we employ a rational Jacobi collocation technique to effectively address linear time-fractional subdiffusion and reaction sub-diffusion equations. The semi-analytic approximation solution, in this case, represents the spatial and temporal variables as a series of rational Jacobi polynomials. Subsequently, we apply the operational collocation method to convert the target equations into a system of algebraic equations. A comprehensive investigation into the convergence properties of the dual series expansion employed in this approximation is conducted, demonstrating the robustness of the numerical method put forth. To illustrate the method's accuracy and practicality, we present several numerical examples. The advantages of this method are: high accuracy, efficiency, applicability, and high rate of convergence.

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Published

2023-10-30

How to Cite

1.
Hafez RM, Youssri YH, Atta AG. Jacobi Rational Operational Approach for Time-Fractional Sub-Diffusion Equation on a Semi-Infinite Domain. Contemp. Math. [Internet]. 2023 Oct. 30 [cited 2024 Jun. 13];4(4):853-76. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3594