Conservative higher-order finite difference scheme for the coupled nonlinear Schrödinger equations

This paper introduces a conservative higher-order finite difference scheme for solving the coupled nonlinear Schrödinger equations. The Crank–Nicolson method is employed to discretize time derivatives and the sixth-order difference operator is used to discretize space derivatives, correspondingly, the resulting difference scheme has second-order accuracy in time and sixth-order accuracy in space. By utilizing the discrete energy method, the conservation of discrete mass and energy, the boundedness, existence and uniqueness of solution, unconditional stability and the convergence of the new scheme are proved. Then making use of Richardson extrapolation, the time accuracy is increased to the fourth order. Finally, the numerical experiments are conducted to validate the theoretical results presented in the paper. •A novel conservative higher-order finite difference method with sixth-order accuracy in space and fourth-order accuracy in time is proposed for solving the coupled nonlinear Schrödinger equations.•The conservation of discrete mass and energy, the boundedness, existence and uniqueness of solution, unconditional stability and the convergence of the new scheme are proved.•Numerical results demonstrate that the presented scheme is superior to the methods in the existing literature in terms of accuracy.