A space-time spectral approximation for solving two dimensional variable-order fractional convection-diffusion equations with nonsmooth solutions

A. Z. Amin (), A. Abdelkawy M.â, M. Soluma E.â and M. Babatin M.â
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A. Z. Amin: Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia
A. Abdelkawy M.â: ��Department of Mathematics and Statistics, College of Science Imam Mohammad Ibn Saud Islamic, University (IMSIU), Riyadh, Saudi Arabia‡Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
M. Soluma E.â: ��Department of Mathematics and Statistics, College of Science Imam Mohammad Ibn Saud Islamic, University (IMSIU), Riyadh, Saudi Arabia‡Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
M. Babatin M.â: ��Department of Mathematics and Statistics, College of Science Imam Mohammad Ibn Saud Islamic, University (IMSIU), Riyadh, Saudi Arabia

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 07, 1-17

Abstract: The study focuses on the numerical solutions of two-dimensional variable-order fractional convection-diffusion equations, which combine the principles of diffusion and convection to describe the movement of particles, energy, other physical quantities within a system. The numerical solution is obtained using shifted Legendre Gauss–Lobatto and shifted Chebyshev Gauss–Radau collocation techniques. The convection-diffusion equation is transformed into a system of algebraic equations utilizing shifted Chebyshev Gauss–Radau and shifted Legendre Gauss–Lobatto nodes. Additionally, numerical test examples are presented to demonstrate the method’s efficacy to handle nonsmooth solutions to the given problems.

Keywords: Variable-order fractional convection-diffusion equations; shifted Legendre and Chebyshev polynomials; Riemann–Liouville fractional of variable order (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0129183124500888

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