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A linearized fourth-order compact ADI method for phytoplankton–zooplankton model arising in marine ecosystem

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Abstract

Mathematical models and numerical simulations have been prominently successful in providing insight for the exploration of evolution mechanism in scientific engineering. In this paper, a linearized fourth-order compact alternating direction implicit (ADI) method is developed to numerically solve a mathematical model, which includes phytoplankton–zooplankton interactions arising in marine ecosystem. The solvability, convergence and stability of the proposed method are discussed as well. It is proven that the proposed method is fourth-order accurate in space and second-order accurate in time. Finally, we present several numerical simulations to confirm the theoretical results.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (No. 12001067), the Macao Young Scholars Program (AM2020016), and the University of Macau (MYRG2019-00009-FST).

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Authors and Affiliations

  1. School of Sciences, Great Bay University, Dongguan, 523000, Guangdong, China

    Gangnan Yuan

  2. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Gangnan Yuan

  3. Department of Mathematics, University of Macau, Taipa, 999078, Macau, China

    Deng Ding & Weiguo Lu

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

    Fengyan Wu

Authors
  1. Gangnan Yuan
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  2. Deng Ding
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  3. Weiguo Lu
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  4. Fengyan Wu
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Correspondence to Fengyan Wu.

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Communicated by Jose Alberto Cuminato.

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Yuan, G., Ding, D., Lu, W. et al. A linearized fourth-order compact ADI method for phytoplankton–zooplankton model arising in marine ecosystem. Comp. Appl. Math. 43, 63 (2024). https://doi.org/10.1007/s40314-023-02570-w

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  • DOI: https://doi.org/10.1007/s40314-023-02570-w

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