A linear, symmetric and energy-conservative scheme for the space-fractional Klein–Gordon–Schrödinger equations. (September 2019)

• Record Type: Journal Article
• Authors: Wang, Ying; Li, Qi; Mei, Liquan
• Is Part Of: Applied mathematics letters. Volume 95(2019)
• Page Start: 104
• Page End: 113
• Publication Date: 2019-09
• Subjects: Space-fractional Klein–Gordon–Schrödinger equations -- Invariant energy quadratization approach -- Crank–Nicolson method -- Fourier spectral method -- Energy conservation; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.03.032
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we propose an efficient numerical scheme for the space-fractional Klein–Gordon–Schrödinger (SFKGS) equations. Motivated by the "Invariant Energy Quadratization" (IEQ) approach, we introduce two auxiliary variables to transform the SFKGS system into a new equivalent system in which the time derivative is discretized by the Crank–Nicolson method, and the space discretization is based on the Fourier spectral method. Consequently, the numerical scheme shares two good features. The first feature is that the nonlinear terms are treated semi-explicitly and a linear symmetric system is solved at each time step. The second feature is the energy conservation at the discrete level. These two advantages are proved by the theoretical analysis and illustrated by a given numerical example.