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

Sarita Nandal, Mahmoud A. Zaky, Rob De Staelen (UGent) and Ahmed S. Hendy
(2021) MATHEMATICS. 9(23).
Author
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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 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.
Keywords
General Mathematics, Engineering (miscellaneous), Computer Science (miscellaneous), nonlinear fractional differential equation of fourth-order, <p>l(2)-1(sigma) formula & nbsp, </p>, two-dimensional, variable coefficients, delay, SUB-DIFFUSION EQUATION, DIFFERENCE SCHEME, PARABOLIC EQUATIONS, APPROXIMATION, DERIVATIVES, ALGORITHM

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MLA
Nandal, Sarita, et al. “Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay.” MATHEMATICS, vol. 9, no. 23, 2021, doi:10.3390/math9233050.
APA
Nandal, S., Zaky, M. A., De Staelen, R., & Hendy, A. S. (2021). Numerical simulation for a multidimensional fourth-order nonlinear fractional subdiffusion model with time delay. MATHEMATICS, 9(23). https://doi.org/10.3390/math9233050
Chicago author-date
Nandal, Sarita, Mahmoud A. Zaky, Rob De Staelen, and Ahmed S. Hendy. 2021. “Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay.” MATHEMATICS 9 (23). https://doi.org/10.3390/math9233050.
Chicago author-date (all authors)
Nandal, Sarita, Mahmoud A. Zaky, Rob De Staelen, and Ahmed S. Hendy. 2021. “Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay.” MATHEMATICS 9 (23). doi:10.3390/math9233050.
Vancouver
1.
Nandal S, Zaky MA, De Staelen R, Hendy AS. Numerical simulation for a multidimensional fourth-order nonlinear fractional subdiffusion model with time delay. MATHEMATICS. 2021;9(23).
IEEE
[1]
S. Nandal, M. A. Zaky, R. De Staelen, and A. S. Hendy, “Numerical simulation for a multidimensional fourth-order nonlinear fractional subdiffusion model with time delay,” MATHEMATICS, vol. 9, no. 23, 2021.
@article{8732333,
  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 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.}},
  articleno    = {{3050}},
  author       = {{Nandal, Sarita and Zaky, Mahmoud A. and De Staelen, Rob and Hendy, Ahmed S.}},
  issn         = {{2227-7390}},
  journal      = {{MATHEMATICS}},
  keywords     = {{General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous),nonlinear fractional differential equation of fourth-order,<p>l(2)-1(sigma) formula & nbsp,</p>,two-dimensional,variable coefficients,delay,SUB-DIFFUSION EQUATION,DIFFERENCE SCHEME,PARABOLIC EQUATIONS,APPROXIMATION,DERIVATIVES,ALGORITHM}},
  language     = {{eng}},
  number       = {{23}},
  pages        = {{15}},
  title        = {{Numerical simulation for a multidimensional fourth-order nonlinear fractional subdiffusion model with time delay}},
  url          = {{http://doi.org/10.3390/math9233050}},
  volume       = {{9}},
  year         = {{2021}},
}
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