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A second-order numerical method for nonlinear variable-order fractional diffusion equation with time delay

Author

Listed:
  • Li, Jing
  • Kang, Xinyue
  • Shi, Xingyun
  • Song, Yufei

Abstract

In this paper, a linearized numerical scheme of nonlinear variable-order fractional diffusion equation with time delay is constructed. We apply the L2−1σ formula to discretize the temporal derivative and second-order central difference scheme to discretize the spatial derivative. The proposed method is unconditionally stable and convergent with Oτ2+h2, where τ and h are the time and space steps, respectively. Numerical experiment demonstrates the effectiveness and accuracy of the numerical scheme.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:219:y:2024:i:c:p:101-111
    DOI: 10.1016/j.matcom.2023.12.019
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    References listed on IDEAS

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    1. Qiang Yu & Viktor Vegh & Fawang Liu & Ian Turner, 2015. "A Variable Order Fractional Differential-Based Texture Enhancement Algorithm with Application in Medical Imaging," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-35, July.
    2. 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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