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Numerical solution of non-linear fourth order fractional sub-diffusion wave equation with time delay

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  • Nandal, Sarita
  • Narain Pandey, Dwijendra

Abstract

In this paper, we constructed a linearized compact difference scheme for fourth order non-linear fractional sub-diffusion equation with time delay and variable coefficients. The primary purpose of our work is to use the idea of the L2−1σ formula for temporal dimension and compact linear operator for spatial dimension. The proposed method is unconditionally stable and convergent to the analytical solution with the order of convergence O(τ2+h4), where τ and h are temporal and spatial lengths, respectively. Numerical experimentation is carried out to show the efficiency and accuracy of the proposed scheme.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308926
    DOI: 10.1016/j.amc.2019.124900
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    References listed on IDEAS

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    1. Wei Gu, 2014. "A Compact Difference Scheme for a Class of Variable Coefficient Quasilinear Parabolic Equations with Delay," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, June.
    2. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
    3. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
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    Cited by:

    1. Heydari, M.H. & Razzaghi, M. & Rouzegar, J., 2022. "Chebyshev cardinal polynomials for delay distributed-order fractional fourth-order sub-diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. 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.
    3. Li, Jing & Kang, Xinyue & Shi, Xingyun & Song, Yufei, 2024. "A second-order numerical method for nonlinear variable-order fractional diffusion equation with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 101-111.

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