Abstract: A new conservative difference scheme is proposed for nonlinear Schrödinger equation, and its convergence and stability are proved. By means of numerical computing, the discretization for nonlinear term of nonlinear Schrödinger equation is discussed, and it is followed that the new difference scheme is better than the scheme of paper[7] which is a special case of the new scheme in precision, when suitable parameter is adopted.

Key words: difference scheme, conservation, convergence, stability