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

In the paper, we give an efficient conservative scheme for the fractional Klein-Gordon-Schrödinger equations, based on the central difference scheme, the Crank-Nicolson scheme and leap-frog scheme. First, we use central difference scheme for discretizing the system in space direction. Second, we use Crank-Nicolson and leap-frog scheme for discretizing the system in time direction. We find that the scheme can be decoupled, linearized and suitable for parallel computation to increase computing efficiency, and preserve mass and energy conservation laws. The convergence of the scheme is discussed, and it is shown that the scheme is of the accuracy O(τ2+h2). The numerical experiments are given, and verify the correctness of theoretical results and the efficiency of the scheme.