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In this paper, several different conserving compact finite difference schemes are developed for solving a class of nonlinear Schrödinger equations with wave operator. It is proved that the numerical solutions are bounded and the numerical methods can achieve a convergence rate of \(\mathcal{O}(\tau^{2} + h^{4})\) in the maximum norm. Moreover, by applying Richardson extrapolation, the proposed methods have a convergence rate of \(\mathcal{O}(\tau^{4} + h^{4})\) in the maximum norm. Finally, several numerical experiments are presented to illustrate the theoretical results.

Several conservative compact schemes for a class of nonlinear Schrödinger equations with wave operator