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An explicit fourth-order energy-preserving scheme for Riesz space fractional nonlinear wave equations

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  • Zhao, Jingjun
  • Li, Yu
  • Xu, Yang

Abstract

In this paper, a new explicit fourth-order scheme for solving Riesz space fractional nonlinear wave equations is developed. The scheme is designed by using a novel Riesz space fractional difference operator for spatial discretization and a multidimensional extended Runge–Kutta–Nyström method for time integration. The conservation law of the semi-discrete energy, stability and convergence of the semi-discrete system are investigated. Numerical experiments show the efficiency and energy conservation of the present scheme.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:351:y:2019:i:c:p:124-138
    DOI: 10.1016/j.amc.2019.01.040
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    References listed on IDEAS

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    1. Cheng, Xiujun & Duan, Jinqiao & Li, Dongfang, 2019. "A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 452-464.
    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. 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. 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.

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