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Fully decoupled, linear, and energy-preserving GSAV difference schemes for the nonlocal coupled sine-Gordon equations in multiple dimensions

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Abstract

In this paper, we intend to utilize the generalized scalar auxiliary variable (GSAV) approach proposed in recent paper (Ju et al., SIAM J. Numer. Anal., 60 (2022), 1905–1931) for the nonlocal coupled sine-Gordon equation to construct a class of fully decoupled, linear, and second-order accurate energy-preserving scheme. The unconditional unique solvability and discrete energy conservation law of the proposed scheme are rigorously discussed, and the unconditional convergence is then proved by the mathematical induction. Particularly, the convergence analysis covers the proposed scheme in multiple dimensions due to the corresponding nonlinear terms satisfy the global Lipschitz continuity straightforwardly. Finally, time evolution of dynamical behavior of the governing equation with different nonlocal parameters are observed, and ample numerical comparisons demonstrate that the proposed scheme manifests high efficiency in long-time computations.

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Acknowledgements

The authors are very grateful to the referees for their valuable comments and suggestions.

Funding

The work is partially supported by the NSFC (Nos. 12171245, 11971242) and the Science and the Technology Research Project of Education Department of Jiangxi Province (No. GJJ2200365). The work of Linghua Kong is supported by the NSFC (No. 11961036) and the Jiangxi Province Natural Science Fund (Nos. 20224ACB201001, 20224BCD41001).

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Authors and Affiliations

  1. Jiangxi Provincial Center for Applied Mathematics, and School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, 330022, China

    Dongdong Hu & Linghua Kong

  2. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

    Wenjun Cai & Yushun Wang

Authors
  1. Dongdong Hu
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  2. Linghua Kong
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  3. Wenjun Cai
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  4. Yushun Wang
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Contributions

Dongdong Hu: formal analysis, writing—original draft. Linghua Kong: review and editing. Wenjun Cai: review and editing. Yushun Wang: supervision, review and editing.

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Correspondence to Yushun Wang.

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Hu, D., Kong, L., Cai, W. et al. Fully decoupled, linear, and energy-preserving GSAV difference schemes for the nonlocal coupled sine-Gordon equations in multiple dimensions. Numer Algor 95, 1953–1980 (2024). https://doi.org/10.1007/s11075-023-01634-6

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  • DOI: https://doi.org/10.1007/s11075-023-01634-6

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