Abstract
In this paper, we propose an alternating direction implicit (ADI) difference method to solve the two-dimensional time-fractional reaction-subdiffusion equation with weakly singular solutions, where L1 scheme on graded mesh is used to capture the initial weak singularity. Global and local convergences of L1-ADI scheme on graded mesh are studied with the comparison principle. The temporal global convergence rate of the fully discrete L1-ADI scheme is \(O(N^{-\min \{ 2-\alpha ,2\alpha ,\alpha r\}})\) and the temporal local convergence rate can attain \(O(N^{-\min \{ 2-\alpha , 2\alpha \}})\) when \(r> 2-\alpha \), where N, \(\alpha \), and r are the time partition number, order of fractional derivative, and grading parameter, respectively. Numerical experiments are proposed to verify the sharpness of our theoretical analysis.
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Acknowledgements
The research is supported in part by Natural Science Foundation of Shandong Province under Grant ZR2023MA077, Fundamental Research Funds for the Central Universities (No. 202264006), and the National Natural Science Foundation of China under Grant 11801026.
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Jiang, Y., Chen, H. Local convergence analysis of L1-ADI scheme for two-dimensional reaction-subdiffusion equation. J. Appl. Math. Comput. 70, 1953–1964 (2024). https://doi.org/10.1007/s12190-024-02037-z
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DOI: https://doi.org/10.1007/s12190-024-02037-z