Shifted fifth-kind Chebyshev polynomials Galerkin-based procedure for treating fractional diffusion-wave equation

A. G. Atta (), W. M. Abd-Elhameed () and Y. H. Youssri
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A. G. Atta: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
W. M. Abd-Elhameed: 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), 2022, vol. 33, issue 08, 1-25

Abstract: Herein, we propose new efficient spectral algorithms for handling the fractional diffusion wave equation (FDWE) and fractional diffusion wave equation with damping (FDWED). In these algorithms, we employ new basis functions of the shifted fifth-kind Chebyshev polynomials that satisfy all the initial and boundary conditions of the equation. The key idea of the presented algorithms depends on transforming the FDWE and FDWED with their underlying conditions into systems of algebraic equations in the unknown expansion coefficients. Our study is supported by a careful convergence analysis of the suggested shifted fifth-kind Chebyshev expansion. Finally, some numerical examples are presented to confirm the accuracy and efficiency of the proposed algorithms.

Keywords: Fractional diffusion wave equation; fifth-kind Chebyshev polynomials; Galerkin method; convergence analysis (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0129183122501029

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