A numerical investigation with energy-preservation for nonlinear space-fractional Klein–Gordon–Schrödinger system

In this paper, we deal with the nonlinear space-fractional Klein–Gordon–Schrödinger system involving the fractional Laplacian operator of order α for 1 < α≤ 2 . We propose an accurate numerical method with eneregy-preserving property for solving the well-known system. The problem is discretized in spatial direction by the Fourier spectral method, and in temporal direction by utilizing the fourth-order exponential time-differencing Runge–Kutta technique. We show that the proposed method satisfies both mass and energy conservation. The convergence of this method is proved, and the order of accuracy is obtained, which shows that the order of convergence is near two. Several numerical experiments are tested to validate the accuracy and reliability of the proposed method. The results are presented in tables and figures for the different values of α that show the proposed method is an efficient framework for solving nonlinear space-fractional Klein–Gordon–Schrödinger system.