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An efficient conservative difference scheme for fractional Klein–Gordon–Schrödinger equations

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  • Wang, Jun-jie
  • Xiao, Ai-guo

Abstract

In the paper, we give an efficient conservative scheme for the fractional Klein–Gordon–Schrödinger equations, based on the central difference scheme, the Crank–Nicolson scheme and leap-frog scheme. First, we use central difference scheme for discretizing the system in space direction. Second, we use Crank–Nicolson and leap-frog scheme for discretizing the system in time direction. We find that the scheme can be decoupled, linearized and suitable for parallel computation to increase computing efficiency, and preserve mass and energy conservation laws. The convergence of the scheme is discussed, and it is shown that the scheme is of the accuracy O(τ2+h2). The numerical experiments are given, and verify the correctness of theoretical results and the efficiency of the scheme.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:691-709
    DOI: 10.1016/j.amc.2017.08.035
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    References listed on IDEAS

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    1. Wang, Dongling & Xiao, Aiguo & Yang, Wei, 2015. "Maximum-norm error analysis of a difference scheme for the space fractional CNLS," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 241-251.
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    Cited by:

    1. Martínez, Romeo & Macías-Díaz, Jorge E. & Sheng, Qin, 2022. "A nonlinear discrete model for approximating a conservative multi-fractional Zakharov system: Analysis and computational simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 1-21.
    2. Yan, Jingye & Zhang, Hong & Liu, Ziyuan & Song, Songhe, 2020. "Two novel linear-implicit momentum-conserving schemes for the fractional Korteweg-de Vries equation," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    3. 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.
    4. Wang, Junjie & Xiao, Aiguo, 2019. "Conservative Fourier spectral method and numerical investigation of space fractional Klein–Gordon–Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 348-365.
    5. Guo, Yantao & Fu, Yayun, 2023. "Two efficient exponential energy-preserving schemes for the fractional Klein–Gordon Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 169-183.

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