A Potent Collocation Approach Based on Shifted Gegenbauer Polynomials for Nonlinear Time Fractional Burgers’ Equations

Authors

  • E. Magdy Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt https://orcid.org/0000-0001-9516-884X
  • W. M. Abd-Elhameed Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt https://orcid.org/0000-0002-6102-671X
  • Y. H. Youssri Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt https://orcid.org/0000-0003-0403-8797
  • G. M. Moatimid 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 https://orcid.org/0000-0003-1467-640X

DOI:

https://doi.org/10.37256/cm.4420233302

Keywords:

Fractional Burgers's equation, Gegenbaur polynomials, spectral methods, error bound

Abstract

This paper presents a numerical strategy for solving the nonlinear time fractional Burgers's equation (TFBE) to obtain approximate solutions of TFBE. During this procedure, the collocation approach is used. The proposed numerical approximations are supposed to be a double sum of the products of two sets of basis functions. The two sets of polynomials are presented here: a modified set of shifted Gegenbauer polynomials and a shifted Gegenbauer polynomial set. Some specific integers and fractional derivatives are explicitly given as a combination of basis functions to apply the proposed collocation procedure. This method transforms the governing boundary-value problem into a set of nonlinear algebraic equations. Newton's approach can be used to solve the resulting nonlinear system. An analysis of the precision of the proposed method is provided. Various examples are presented and compared to some existing methods in the literature to prove the reliability of the suggested approach.

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Published

2023-10-07

How to Cite

1.
Magdy E, Abd-Elhameed WM, Youssri YH, Moatimid GM, Atta AG. A Potent Collocation Approach Based on Shifted Gegenbauer Polynomials for Nonlinear Time Fractional Burgers’ Equations. Contemp. Math. [Internet]. 2023 Oct. 7 [cited 2024 May 25];4(4):647-65. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3302