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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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