Numerical simulation of a nonlinearly coupled Schrödinger system: A linearly uncoupled finite difference scheme

This article describes a finite difference scheme which is linearly uncoupled in computation for a nonlinearly coupled Schrödinger system. This numerical scheme is proved to preserve the original conservative properties. Using the discrete energy analysis method, we also prove that the scheme is unconditionally stable and second-order convergent in discrete L2-norm based on some preliminary estimations. The results show that the new scheme is efficiency.