New conservative difference schemes for a coupled nonlinear Schrödinger system

Abstract In this paper, two conservative difference schemes for solving a coupled nonlinear Schrodinger (CNLS) system are numerically analyzed. Firstly, a nonlinear implicit two-level finite difference scheme for CNLS system is studied, then a linear three-level difference scheme for CNLS system is presented. An induction argument and the discrete energy method are used to prove the second-order convergence and unconditional stability of the linear scheme. Numerical examples show the efficiency of the new scheme.

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