Abstract This paper is concerned with the numerical solutions of nonlinear Schrodinger equation (NLSE) in one-dimensional unbounded domain. The unbounded problem is truncated by the third-order absorbing boundary conditions (ABCs), and the corresponding initial-boundary value problem is solved by a three-level linearized difference scheme. By introducing auxiliary functions to simplify the difference scheme, the proposed difference scheme for NLSE with third-order ABCs is theoretically analyzed. It is strictly proved that the difference scheme is uniquely solvable and unconditionally stable, and has second-order accuracy both in time and space. Finally, several numerical examples are given to verify the theoretical results.

中文翻译：

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具有吸收边界条件的非线性薛定谔方程的三级线性差分格式

摘要 本文研究了一维无界域中非线性薛定谔方程(NLSE)的数值解。无界问题由三阶吸收边界条件 (ABCs) 截断，相应的初边界值问题由三级线性化差分格式求解。通过引入辅助函数来简化差分格式，从理论上分析了所提出的具有三阶ABC的NLSE差分格式。严格证明该差分格式是唯一可解且无条件稳定的，在时间和空间上均具有二阶精度。最后给出了几个数值例子来验证理论结果。