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

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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)

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.

Suggested Citation

  • Ahmed Gamal Atta & Waleed Mohamed Abd-Elhameed & Galal Mahrous Moatimid & Youssri Hassan Youssri, 2022. "A Fast Galerkin Approach for Solving the Fractional Rayleigh–Stokes Problem via Sixth-Kind Chebyshev Polynomials," Mathematics, MDPI, vol. 10(11), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1843-:d:825588
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    References listed on IDEAS

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    1. Zhou, Fengying & Xu, Xiaoyong, 2016. "The third kind Chebyshev wavelets collocation method for solving the time-fractional convection diffusion equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 11-29.
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