Energy-preserving scheme for the nonlinear fractional Klein-Gordon Schrodinger equation

This paper introduces the energy-preserving scheme for the nonlinear fractional Klein-Gordon Schrodinger 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. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

This paper presents an energy-preserving scheme for the nonlinear fractional Klein-Gordon Schrodinger equation using the scalar auxiliary variable approach. By introducing a scalar variable, the system is transformed into a new equivalent system, and a linear implicit energy-preserving scheme is obtained by applying the extrapolated Crank-Nicolson method in the temporal direction and Fourier pseudospectral method in the spatial direction.