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An explicit fourth-order energy-preserving difference scheme for the Riesz space-fractional Sine–Gordon equations

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  • Xing, Zhiyong
  • Wen, Liping
  • Wang, Wansheng

Abstract

In this paper, we study the numerical solution of the Riesz space fractional Sine–Gordon equations. We develop an explicit fourth-order energy-preserving difference scheme for the two-dimensional space fractional Sine–Gordon equation (SGE). The conservation, convergence and boundedness properties of the numerical scheme are rigorously proved. Subsequently, the proposed numerical method is applied to approximate the one-dimensional space fractional SGE. Several numerical experiments are provided to verify the theoretical results.

Suggested Citation

  • Xing, Zhiyong & Wen, Liping & Wang, Wansheng, 2021. "An explicit fourth-order energy-preserving difference scheme for the Riesz space-fractional Sine–Gordon equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 624-641.
    • Handle: RePEc:eee:matcom:v:181:y:2021:i:c:p:624-641
    DOI: 10.1016/j.matcom.2020.10.008
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    References listed on IDEAS

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    1. Jiang, Chaolong & Sun, Jianqiang & Li, Haochen & Wang, Yifan, 2017. "A fourth-order AVF method for the numerical integration of sine-Gordon equation," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 144-158.
    2. Xing, Zhiyong & Wen, Liping, 2019. "Numerical analysis and fast implementation of a fourth-order difference scheme for two-dimensional space-fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 155-166.
    3. Wang, Jun-jie & Xiao, Ai-guo, 2018. "An efficient conservative difference scheme for fractional Klein–Gordon–Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 691-709.
    4. Zhao, Jingjun & Li, Yu & Xu, Yang, 2019. "An explicit fourth-order energy-preserving scheme for Riesz space fractional nonlinear wave equations," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 124-138.
    5. Macías-Díaz, J.E. & Hendy, A.S. & De Staelen, R.H., 2018. "A compact fourth-order in space energy-preserving method for Riesz space-fractional nonlinear wave equations," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 1-14.
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    Cited by:

    1. Almushaira, Mustafa, 2023. "Efficient energy-preserving eighth-order compact finite difference schemes for the sine-Gordon equation," Applied Mathematics and Computation, Elsevier, vol. 451(C).

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