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

Yubing Jiang, Hu Chen, Tao Sun and Chaobao Huang

Applied Mathematics and Computation, 2024, vol. 471, issue C

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.

Keywords: ADI method; L1 scheme; Nonlinear subdiffusion; Pointwise-in-time error estimate (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:471:y:2024:i:c:s009630032400081x

DOI: 10.1016/j.amc.2024.128609

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