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

Abstract

Abstract 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 O(τ2+h4) $\mathcal{O}(\tau^{2} + h^{4})$ in the maximum norm. Moreover, by applying Richardson extrapolation, the proposed methods have a convergence rate of O(τ4+h4) $\mathcal{O}(\tau^{4} + h^{4})$ in the maximum norm. Finally, several numerical experiments are presented to illustrate the theoretical results.

Keywords

• Nonlinear Schrödinger equations with wave operator
• Discrete conservation laws
• Stability
• Convergence