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

Author

Listed:
  • 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
    Department of Applied Mathematics, National Research Centre, Dokki, Cairo 12622, Egypt)

  • Rob H. De Staelen

    (Beheer en Algemene Directie, Ghent University Hospital, C. Heymanslaan 10, 9000 Ghent, Belgium
    Dean’s Office of the Faculty of Medicine and Health Sciences, Ghent University, C. Heymanslaan 10, 9000 Ghent, Belgium)

  • Ahmed S. Hendy

    (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., 620002 Yekaterinburg, Russia)

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.

Suggested Citation

  • Sarita Nandal & Mahmoud A. Zaky & Rob H. De Staelen & Ahmed S. Hendy, 2021. "Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3050-:d:689542
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    References listed on IDEAS

    as
    1. Pu, Zhe & Ran, Maohua & Luo, Hong, 2021. "Fast and high-order difference schemes for the fourth-order fractional sub-diffusion equations with spatially variable coefficient under the first Dirichlet boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 110-133.
    2. Hendy, Ahmed S. & Zaky, Mahmoud A. & Suragan, Durvudkhan, 2022. "Discrete fractional stochastic Grönwall inequalities arising in the numerical analysis of multi-term fractional order stochastic differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 269-279.
    3. Hendy, Ahmed S. & Zaky, Mahmoud A. & Abbaszadeh, Mostafa, 2021. "Long time behavior of Robin boundary sub-diffusion equation with fractional partial derivatives of Caputo type in differential and difference settings," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1370-1378.
    4. Zhang, Jinghua & Liu, Fawang & Lin, Zeng & Anh, Vo, 2019. "Analytical and numerical solutions of a multi-term time-fractional Burgers’ fluid model," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 1-12.
    5. Cheng, Xiujun & Duan, Jinqiao & Li, Dongfang, 2019. "A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 452-464.
    6. Nandal, Sarita & Narain Pandey, Dwijendra, 2020. "Numerical solution of non-linear fourth order fractional sub-diffusion wave equation with time delay," Applied Mathematics and Computation, Elsevier, vol. 369(C).
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    Cited by:

    1. Songkran Pleumpreedaporn & Weerawat Sudsutad & Chatthai Thaiprayoon & Juan E. Nápoles & Jutarat Kongson, 2021. "A Study of ψ -Hilfer Fractional Boundary Value Problem via Nonlinear Integral Conditions Describing Navier Model," Mathematics, MDPI, vol. 9(24), pages 1-31, December.

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