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A second-order finite difference scheme for nonlinear tempered fractional integrodifferential equations in three dimensions

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Abstract

In this paper, we provide a numerical solution for the nonlinear tempered fractional integrodifferential equation in three dimensions. We use the trapezoidal convolution rule with backward differences (BDF2) for temporal discretization, and develop an alternating direction implicit difference scheme for spatial discretization. A novel fast approximation is applied to tackle the nonlinear term. The stability and convergence analysis of the numerical scheme are analyzed. Furthermore, some numerical experiments are provided to confirm the theoretical results.

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Acknowledgements

The authors thank the anonymous reviewers for their constructive comments and suggestions. We also thank Professor Yubin Yan for stimulating discussions and for his constant encouragement and support.

Funding

This work is supported by the National Natural Science Foundation of China (12101080) and Scientific Research Foundation of Hunan Provincial Education Department (21C0188). Hunan Provincial Natural Science Foundation of China (2022JJ40463). Postgraduate Scientific Research Innovation Project of Hunan Province (CX20220955). National foreign expert introduction foundation (G2022004016L). A. S. Hendy wishes to acknowledge the support of the RSF, Russia grant, project 22-21-00075.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan, 410114, People’s Republic of China

    R. Wang

  2. School of Mathematical Sciences, Shanxi University, Shanxi, Taiyuan, 030006, People’s Republic of China

    L. Qiao

  3. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

    M. A. Zaky

  4. Department of Applied Mathematics, National Research Centre, Dokki, Cairo, 12622, Egypt

    M. A. Zaky

  5. Department of Applied Mathematics, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., Yekaterinburg, 620002, Russia

    A. S. Hendy

  6. Department of Mathematics, Faculty of Science, Benha University, Benha, 13511, Egypt

    A. S. Hendy

Authors
  1. R. Wang
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  2. L. Qiao
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  3. M. A. Zaky
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  4. A. S. Hendy
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Correspondence to L. Qiao, M. A. Zaky or A. S. Hendy.

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Wang, R., Qiao, L., Zaky, M.A. et al. A second-order finite difference scheme for nonlinear tempered fractional integrodifferential equations in three dimensions. Numer Algor 95, 319–349 (2024). https://doi.org/10.1007/s11075-023-01573-2

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  • DOI: https://doi.org/10.1007/s11075-023-01573-2

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