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Discrete comparison principle of a finite difference method for the multi-term time fractional diffusion equation

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Abstract

A discrete comparison principle is given for the multi-term time fractional diffusion equation, where the discrete scheme is based on L1 approximation of the multi-term temporal Caputo derivative and the standard finite difference approximation of the spatial derivative. Then we use the discrete comparison principle to give an error analysis of the discrete scheme by constructing a barrier function. The final numerical results verify our theoretical analysis under the realistic assumption that the solution of the time fractional diffusion equation has a weak singularity near the initial time t = 0.

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All data included in this study are available upon reasonable request.

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Funding

This work is supported in part by the National Natural Science Foundation of China under Grant 11801026, and Fundamental Research Funds for the Central Universities (No. 202264006).

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Authors and Affiliations

  1. School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, China

    Yue Wang & Hu Chen

  2. Network and Information Center, Ocean University of China, Qingdao, 266100, China

    Youxing Zhao

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  1. Yue Wang
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  2. Youxing Zhao
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  3. Hu Chen
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Correspondence to Hu Chen.

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Wang, Y., Zhao, Y. & Chen, H. Discrete comparison principle of a finite difference method for the multi-term time fractional diffusion equation. Numer Algor 93, 1581–1593 (2023). https://doi.org/10.1007/s11075-022-01480-y

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