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

Longbin Wu, Qiang Ma and Xiaohua Ding

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 190, issue C, 1110-1129

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.

Keywords: Nonlinear fractional Klein–Gordon Schrödinger equation; CN-SAV; Conservation of mass and energy; Convergence (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:190:y:2021:i:c:p:1110-1129

DOI: 10.1016/j.matcom.2021.07.003

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