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

A. Z. Amin (), M. A. Abdelkawy and I. Hashim
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A. Z. Amin: Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia
M. A. Abdelkawy: ��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
I. Hashim: Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

International Journal of Modern Physics C (IJMPC), 2023, vol. 34, issue 03, 1-14

Abstract: One of the problems in the numerical analysis of solutions is the nonlinear variable-order fractional convection-diffusion equations for nonsmooth solutions. We offer a numerical technique based on the shifted Legendre Gauss-Lobatto collocation and the shifted Chebyshev Gauss-Radau collocation to solve the problem. The technique with shifted Legendre Gauss-Lobatto and shifted Chebyshev Gauss-Radau nodes is applied to diminish nonlinear variable-order fractional convection-diffusion equations to an easily-solvable system of algebraic equations. Besides, we give numerical test examples to show that the approach can preserve the nonsmooth solution of the underlying problems.

Keywords: Riemann–Liouville fractional of variable order; fractional calculus; spectral collocation method; shifted Legendre and Chebyshev polynomials (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0129183123500419

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