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

• Published in: Mathematics (Basel) Vol. 9; no. 23; p. 3050
• Main Authors: Nandal, Sarita, Zaky, Mahmoud A., De Staelen, Rob H., Hendy, Ahmed S.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-12-2021
• Subjects: Approximation; Boundary conditions; delay; Delay time; Finite difference method; Finite element analysis; Finite volume method; Food science; L2 − 1σ formula; Mathematical models; nonlinear fractional differential equation of fourth-order; Partial differential equations; Time constant; Time lag; two-dimensional; variable coefficients
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math9233050

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 L2−1σ 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.