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Conservative Fourier spectral method and numerical investigation of space fractional Klein–Gordon–Schrödinger equations

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  • Wang, Junjie
  • Xiao, Aiguo

Abstract

In this paper, we propose Fourier spectral method to solve space fractional Klein–Gordon–Schrödinger equations with periodic boundary condition. First, the semi-discrete scheme is given by using Fourier spectral method in spatial direction, and conservativeness and convergence of the semi-discrete scheme are discussed. Second, the fully discrete scheme is obtained based on Crank–Nicolson/leap-frog methods in time direction. It is shown that the scheme can be decoupled, and preserves mass and energy conservation laws. It is proven that the scheme is of the accuracy O(τ2+N−r). Last, based on the numerical experiments, the correctness of theoretical results is verified, and the effects of the fractional orders α, β on the solitary solution behaviors are investigated. In particular, some interesting phenomena including the quantum subdiffusion are observed, and complex dynamical behaviors are shown clearly by many intuitionistic images.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:350:y:2019:i:c:p:348-365
    DOI: 10.1016/j.amc.2018.12.046
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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.
    2. 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.
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    Cited by:

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    2. Wu, Longbin & Ma, Qiang & Ding, Xiaohua, 2021. "Energy-preserving scheme for the nonlinear fractional Klein–Gordon Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1110-1129.
    3. Li, Meng & Fei, Mingfa & Wang, Nan & Huang, Chengming, 2020. "A dissipation-preserving finite element method for nonlinear fractional wave equations on irregular convex domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 404-419.
    4. Huang, Qiong-Ao & Zhang, Gengen & Wu, Bing, 2022. "Fully-discrete energy-preserving scheme for the space-fractional Klein–Gordon equation via Lagrange multiplier type scalar auxiliary variable approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 265-277.
    5. 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).
    6. 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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