A linearized energy-conservative scheme for two-dimensional nonlinear Schrödinger equation with wave operator

作者：

Highlights：

• Based on the invariant energy quadratization approach, a linear implicit and local energy preserving scheme for the nonlinear Schrödinger equation with wave operator is introduced.

• The real form of nonlinear Schrödinger equation with wave operator is reformulated into an equivalent system by introducing some auxiliary variables.

• The equivalent system is discretized by the finite difference method to yield a linear system at each time step, which can be efficiently solved.

• A numerical analysis of the proposed scheme is conducted to show its uniquely solvability and convergence.

摘要

•Based on the invariant energy quadratization approach, a linear implicit and local energy preserving scheme for the nonlinear Schrödinger equation with wave operator is introduced.•The real form of nonlinear Schrödinger equation with wave operator is reformulated into an equivalent system by introducing some auxiliary variables.•The equivalent system is discretized by the finite difference method to yield a linear system at each time step, which can be efficiently solved.•A numerical analysis of the proposed scheme is conducted to show its uniquely solvability and convergence.

论文关键词：Nonlinear Schrödinger equation with wave operator,Invariant energy quadratization,Energy preserving scheme,Stability

论文评审过程：Received 20 October 2020, Revised 17 February 2021, Accepted 19 March 2021, Available online 3 April 2021, Version of Record 3 April 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126234