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A fully discrete GL-ADI scheme for 2D time-fractional reaction-subdiffusion equation

Author

Listed:
  • Jiang, Yubing
  • Chen, Hu
  • Huang, Chaobao
  • Wang, Jian

Abstract

Alternating direction implicit (ADI) difference method for solving a 2D reaction-subdiffusion equation whose solution behaves a weak singularity at t=0 is studied in this paper. A Grünwald-Letnikov (GL) approximation is used for the discretization of Caputo fractional derivative (of order α, with 0<α<1) on a uniform mesh. Stability and convergence of the fully discrete ADI scheme are rigorously established. With the help of a discrete fractional Gronwall inequality, we get the sharp error estimate. The stability in L2 norm and the convergence of the GL-ADI scheme are strictly proved, where the convergent order is O(τtsα−1+τ2α+h12+h22). Numerical experiments are given to verify the theoretical analysis.

Suggested Citation

  • Jiang, Yubing & Chen, Hu & Huang, Chaobao & Wang, Jian, 2025. "A fully discrete GL-ADI scheme for 2D time-fractional reaction-subdiffusion equation," Applied Mathematics and Computation, Elsevier, vol. 488(C).
    • Handle: RePEc:eee:apmaco:v:488:y:2025:i:c:s0096300324006088
    DOI: 10.1016/j.amc.2024.129147
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    References listed on IDEAS

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    1. Kamran Zakaria & Saeed Hafeez, 2020. "Options Pricing for Two Stocks by Black Sholes Time Fractional Order NonLinear Partial Differential Equation," Papers 2010.13411, arXiv.org.
    2. Chatterjee, Amar Nath & Ahmad, Bashir, 2021. "A fractional-order differential equation model of COVID-19 infection of epithelial cells," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
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