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A Linearized Compact ADI Scheme for Semilinear Parabolic Problems with Distributed Delay

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Abstract

Effective compact alternating direction implicit (ADI) schemes are developed for solving the semilinear parabolic problems with distributed delay. Solvability, convergence and stability of the proposed linearized schemes are studied. After that, the schemes are applied to simulate several biological models. It is shown that the obtained numerical schemes produce better convergent results than the usual ADI method, without increasing extra computational cost. The numerical results fit well the theoretical findings.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Hongyu Qin

  2. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    Fengyan Wu

  3. Department of Mathematics, University of Macau, Macao, China

    Fengyan Wu

  4. School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China

    Jiwei Zhang

  5. College of Mathematics and Statistics, and Chongqing Key Laboratory of Analytic Mathematics and Applications, Chongqing University, Chongqing, 401331, China

    Chunlai Mu

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  1. Hongyu Qin
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  2. Fengyan Wu
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  3. Jiwei Zhang
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  4. Chunlai Mu
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Correspondence to Fengyan Wu.

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This work is supported by NSFC (Grant Nos. 11771162, 12001067, 11771035, 11771062, 11971082), the Fundamental Research Funds for the Central Universities (Project No. 2019CDXYST0015, 2019CDJCYJ001, 2020CDJQY-Z001), China Postdoctoral Science Foundation funded project No. 2019M653333, and Natural Science Foundation of Chongqing, China, No. cstc2019jcyj-bshX0038.

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Qin, H., Wu, F., Zhang, J. et al. A Linearized Compact ADI Scheme for Semilinear Parabolic Problems with Distributed Delay. J Sci Comput 87, 25 (2021). https://doi.org/10.1007/s10915-021-01441-y

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  • DOI: https://doi.org/10.1007/s10915-021-01441-y

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