An Efficient Hybrid Numerical Scheme for Nonlinear Multiterm Caputo Time and Riesz Space Fractional-Order Diffusion Equations with Delay
Omran A.K. Zaky M.A. Hendy A.S. Pimenov V.G.
2021Hindawi Limited
Journal of Function Spaces
2021#2021
In this paper, we construct and analyze a linearized finite difference/Galerkin-Legendre spectral scheme for the nonlinear multiterm Caputo time fractional-order reaction-diffusion equation with time delay and Riesz space fractional derivatives. The temporal fractional orders in the considered model are taken as 0<β0<β1<β2<⋯<βm<1. The problem is first approximated by the L1 difference method on the temporal direction, and then, the Galerkin-Legendre spectral method is applied on the spatial discretization. Armed by an appropriate form of discrete fractional Grönwall inequalities, the stability and convergence of the fully discrete scheme are investigated by discrete energy estimates. We show that the proposed method is stable and has a convergent order of 2-βm in time and an exponential rate of convergence in space. We finally provide some numerical experiments to show the efficacy of the theoretical results.
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Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., Yekaterinburg, 620002, Russian Federation
Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, 71524, Egypt
Department of Mathematics, Nazarbayev University, Nur-Sultan, Kazakhstan
Department of Applied Mathematics, Physics Division, National Research Centre, Dokki, Cairo, 12622, Egypt
Department of Mathematics, Faculty of Science, Benha University, Benha, 13511, Egypt
Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 Kovalevskoy St., Yekaterinburg, 620000, Russian Federation
Department of Computational Mathematics and Computer Science
Department of Mathematics
Department of Mathematics
Department of Applied Mathematics
Department of Mathematics
Institute of Mathematics and Mechanics
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