An efficient conservative difference scheme for fractional Klein–Gordon–Schrödinger equations

Structure-preserving algorithms for the two-dimensional fractional Klein-Gordon-Schrödinger equation

“…Recently, some scholars studied structure-preserving numerical schemes for the one-dimensional fractional KGS equation. For instance, Wang and Xiao developed a conservative difference scheme [7] for the equation with Dirichlet boundary condition. In Ref.…”

Conservative finite difference methods for fractional Schrödinger–Boussinesq equations and convergence analysis

“…Han et al [17] established the global well-posedness for the Cauchy problem of fractional SBq (FSBq) equations in H s (R), s ≥ 1. In recent years, there are various numerical methods in the numerical analysis and scientific computing for FSE, including finite difference method [18][19][20][21][22][23], finite element method [24,25], spectral method [26] and collocation method [27].…”

“…In [35], a TSFS method and a finite difference method for the Riesz FSBq equations were considered. In addition, for the similar coupled fractional Klein-Gordon-Schrödinger equations, a conservative difference scheme was formulated in [23], which can be used for reference. To the best of our knowledge, the work done on the numerical methods for solving FSBq equations is so far quite limited.…”

A Fourier spectral method for the nonlinear coupled space fractional Klein‐Gordon‐Schrödinger equations

“…[30][31][32][33][34] Simultaneously, some numerical methods were developed to solve the fractional Klein-Gordon equations. [35][36][37][38] Wang et al investigated an efficient conservative difference scheme for the nonlinear coupled space fractional Klein-Gordon-Schrödinger (NCSFKGS) equations in [39]. Over the past 30 years, Fourier spectral method has been actively applied to solve integer partial differential equations.…”

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In this paper, we give an efficient numerical method for the nonlinear coupled space fractional Klein-Gordon-Schrödinger (NCSFKGS) equations, based on the Crank-Nicolson method, the central difference method and the Fourier spectral method. As far as we know, no one has studied the Equations (5)-(6) in our paper, these equations are different from those in [39] which only considers space fractional Schrödinger equation while the Klein-Gordon equation is classical, here, we consider the two equations which are both space fractional. In this paper, the Crank-Nicolson method and the central difference method are used to discretize the space fractional Schrödinger equation and the space fractional Klein-Gordon equation in time direction, respectively.

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