A conservative numerical method for a class of unstable nonlinear Schrödinger equation

This paper is concerned with the numerical solution to a class of unstable nonlinear Schrödinger equations. A conservative numerical scheme is devised, and three of its discrete conservation laws are proved. Meanwhile, stability and convergence of such scheme with second order convergence rate of time and space are proved by the energy method. In addition, a numerical example is given to demonstrate the accuracy and efficiency of the proposed method.