A Fast Galerkin Approach for Solving the Fractional Rayleigh–Stokes Problem via Sixth-Kind Chebyshev Polynomials

Ahmed Gamal Atta, Waleed Mohamed Abd-Elhameed, Galal Mahrous Moatimid and Youssri Hassan Youssri
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Ahmed Gamal Atta: Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11566, Egypt
Waleed Mohamed Abd-Elhameed: Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
Galal Mahrous Moatimid: Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11566, Egypt
Youssri Hassan Youssri: Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

Mathematics, 2022, vol. 10, issue 11, 1-16

Abstract: Herein, a spectral Galerkin method for solving the fractional Rayleigh–Stokes problem involving a nonlinear source term is analyzed. Two kinds of basis functions that are related to the shifted sixth-kind Chebyshev polynomials are selected and utilized in the numerical treatment of the problem. Some specific integer and fractional derivative formulas are used to introduce our proposed numerical algorithm. Moreover, the stability and convergence accuracy are derived in detail. As a final validation of our theoretical results, we present a few numerical examples.

Keywords: fractional differential equations; orthogonal polynomials; spectral methods; convergence analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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