Abstract: In this paper, the authors propose a three-level and linear difference scheme through adding a dissipation term to the nonlinear Schr\"{o}dinger equation. It is proved that the scheme preserves two conservative quantities that the continuous equation owns. Comparing it with the known schemes by the numerical examples, the authors get the conclusion that the scheme is computed easily and has higher precision.

Key words: NLS equation, Dissipation, Difference scheme, Convergence, Stability.