Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay

Sarita Nandal, Mahmoud A. Zaky, Rob H. De Staelen and Ahmed S. Hendy
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Sarita Nandal: Technology Studies Department, Woosong University, Jayang-Dong, Dong-Gu, Daejeon 300-718, Korea
Mahmoud A. Zaky: Department of Mathematics, Nazarbayev University, Nur-Sultan 010000, Kazakhstan
Rob H. De Staelen: Beheer en Algemene Directie, Ghent University Hospital, C. Heymanslaan 10, 9000 Ghent, Belgium
Ahmed S. Hendy: Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt

Mathematics, 2021, vol. 9, issue 23, 1-15

Abstract: The purpose of this paper is to develop a numerical scheme for the two-dimensional fourth-order fractional subdiffusion equation with variable coefficients and delay. Using the L 2 − 1 σ approximation of the time Caputo derivative, a finite difference method with second-order accuracy in the temporal direction is achieved. The novelty of this paper is to introduce a numerical scheme for the problem under consideration with variable coefficients, nonlinear source term, and delay time constant. The numerical results show that the global convergence orders for spatial and time dimensions are approximately fourth order in space and second-order in time.

Keywords: nonlinear fractional differential equation of fourth-order; L 2 ? 1 ? formula; two-dimensional; variable coefficients; delay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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