On HSS-like iteration method for the space fractional coupled nonlinear Schrödinger equations

The implicit conservative difference scheme with the fractional centered difference formula, which is unconditionally stable, is employed to discretize the space fractional coupled nonlinear Schrödinger equations. The coefficient matrix of the discretized linear system is equal to the sum of a complex scaled identity matrix which can be written as the imaginary unit times the identity matrix and a symmetric diagonal-plus-Toeplitz matrix. In this paper, the HSS-like iteration method is proposed to solve the discretized linear system. Theoretical analyses show that the HSS-like iteration method is unconditionally convergent. Numerical examples are presented to illustrate the effectiveness of the HSS-like iteration method.