An L1 type difference/Galerkin spectral scheme for variable-order time-fractional nonlinear diffusion–reaction equations with fixed delay
Zaky M.A. Van Bockstal K. Taha T.R. Suragan D. Hendy A.S.
1 March 2023Elsevier B.V.
Journal of Computational and Applied Mathematics
2023#420
A linearized spectral Galerkin/finite difference approach is developed for variable fractional-order nonlinear diffusion–reaction equations with a fixed time delay. The temporal discretization for the variable-order fractional derivative is performed by the L1-approximation. An appropriate basis function in terms of Legendre polynomials is used to construct the Galerkin spectral method for the spatial discretization of the second-order spatial operator. The main advantage of the proposed approach is that the implementation of the iterative process is avoided for the nonlinear term in the variable fractional-order problem. Convergence and stability estimates for the constructed scheme are proved theoretically by discrete energy estimates. Some numerical experiments are finally provided to demonstrate the efficiency and accuracy of the theoretical findings.
Convergence and stability estimates , Galerkin spectral method , L1 difference scheme , Time delay , Variable order diffusion
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Department of Applied Mathematics, National Research Centre, Dokki, 33 El-Bohouth St., Giza, 12622, Egypt
, Department of Electronics and Information systems, Ghent University, Krijgslaan 281, Ghent, 9000, Belgium
Department of Computer Science, University of Georgia, Athens, 30602-7404, GA, United States
Department of Mathematics, Nazarbayev University, Nur-Sultan, Kazakhstan
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, Benha University, Benha, 13511, Egypt
Department of Applied Mathematics
, Department of Electronics and Information systems, Ghent University, Krijgslaan 281, Ghent, 9000, Belgium
Department of Computer Science
Department of Mathematics
Department of Computational Mathematics and Computer Science
Department of Mathematics
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