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Energy-preserving scheme for the nonlinear fractional Klein–Gordon Schrödinger equation

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  • Wu, Longbin
  • Ma, Qiang
  • Ding, Xiaohua

Abstract

This paper introduces the energy-preserving scheme for the nonlinear fractional Klein–Gordon Schrödinger equation, which uses the scalar auxiliary variable approach. By a scalar variable, the system is transformed into a new equivalent system. Then applying the extrapolated Crank–Nicolson method on the temporal direction and Fourier pseudospectral method on space direction, we give a linear implicit energy-preserving scheme. Moreover, it proved that at each discrete time the scheme preserves the corresponding discrete mass and energy. The unique solvability and convergence of the numerical solution are also investigated. In particular, it shows the method has the second-order accuracy in time and the spectral accuracy in space. Finally, it gives the algorithm implementation. Several numerical examples illustrate the efficiency and accuracy of the numerical scheme.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:1110-1129
    DOI: 10.1016/j.matcom.2021.07.003
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    References listed on IDEAS

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    1. Li, Dongfang & Zhang, Chengjian, 2020. "Long time numerical behaviors of fractional pantograph equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 244-257.
    2. 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.
    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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