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Efficient L1-ADI finite difference method for the two-dimensional nonlinear time-fractional diffusion equation

Author

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  • Jiang, Yubing
  • Chen, Hu
  • Sun, Tao
  • Huang, Chaobao

Abstract

In this work, we propose an efficient finite difference method for the two-dimensional nonlinear time-fractional diffusion equation with weakly singular solutions. By using backward formula for the approximation of nonlinear term, and L1 scheme on uniform mesh for discretisation of temporal Caputo fractional derivative, a linear scheme is constructed and analysed. Stability and pointwise-in-time convergence of the fully discrete scheme are rigorously established. Numerical results are provided to confirm the sharpness of theoretical analysis.

Suggested Citation

  • Jiang, Yubing & Chen, Hu & Sun, Tao & Huang, Chaobao, 2024. "Efficient L1-ADI finite difference method for the two-dimensional nonlinear time-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 471(C).
    • Handle: RePEc:eee:apmaco:v:471:y:2024:i:c:s009630032400081x
    DOI: 10.1016/j.amc.2024.128609
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    Keywords

    ADI method; L1 scheme; Nonlinear subdiffusion; Pointwise-in-time error estimate;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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