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L1 Method on Nonuniform Meshes for Linear Time-Fractional Diffusion Equations with Constant Time Delay

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Abstract

This paper is concerned with numerical solution of the linear time-fractional diffusion equations with constant time delay. First we investigate the existence, uniqueness and regularity of the exact solution of such equations. Focusing on the time derivative discontinuities behavior of the solutions of the equations at multiple points generated by the time delay and the Caputo fractional derivative, we propose a numerical method based on the L1 method on time nonuniform meshes and the standard finite element method in space. Moreover, the results of stability and error estimate for the method are obtained under the regularity condition. The validity of the proposed method is verified by numerical experiments.

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Authors and Affiliations

  1. School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering & National Center for Applied Mathematics in Hunan, Xiangtan University, Xiangtan, Hunan, 411105, People’s Republic of China

    Tan Tan, Wei-Ping Bu & Ai-Guo Xiao

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  1. Tan Tan
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  2. Wei-Ping Bu
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Correspondence to Ai-Guo Xiao.

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This research is supported by the National Natural Science Foundation of China (Grant No. 12071403) and the Research Foundation of Education Commission of Hunan Province of China (Nos. 21A0108, 19B565).

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Tan, T., Bu, WP. & Xiao, AG. L1 Method on Nonuniform Meshes for Linear Time-Fractional Diffusion Equations with Constant Time Delay. J Sci Comput 92, 98 (2022). https://doi.org/10.1007/s10915-022-01948-y

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  • DOI: https://doi.org/10.1007/s10915-022-01948-y

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