Numerical simulation for a multidimensional fourth-order nonlinear fractional subdiffusion model with time delay

Nandal S. Zaky M.A. De Staelen R.H. Hendy A.S.
December-1 2021 MDPI

Mathematics
2021 #9 Issue 23

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 L₂ − 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.

Delay , L2 two-dimensional , Nonlinear fractional differential equation of fourth-order , Variable coefficients

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Technology Studies Department, Woosong University, Jayang-Dong, Dong-Gu, Daejeon, 300-718, South Korea
Department of Mathematics, Nazarbayev University, Nur-Sultan, 010000, Kazakhstan
Department of Applied Mathematics, National Research Centre, Dokki, Cairo, 12622, Egypt
Beheer en Algemene Directie, Ghent University Hospital, C. Heymanslaan 10, Ghent, 9000, Belgium
Dean’s Office of the Faculty of Medicine and Health Sciences, Ghent University, C. Heymanslaan 10, Ghent, 9000, Belgium
Department of Mathematics, Faculty of Science, Benha University, Benha, 13511, Egypt
Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., Yekaterinburg, 620002, Russian Federation

Technology Studies Department
Department of Mathematics
Department of Applied Mathematics
Beheer en Algemene Directie
Dean’s Office of the Faculty of Medicine and Health Sciences
Department of Mathematics
Department of Computational Mathematics and Computer Science

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