A three-level linearized difference scheme for nonlinear Schrodinger equation with absorbing boundary conditions

被引：4

作者：

Pan, Kejia ^{[1
]}

Xia, Junyi ^{[1
,2
]}

He, Dongdong ^{[3
]}

Zhang, Qifeng ^{[4
]}

机构：

[1] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[3] Chinese Univ Hong Kong, Sch Sci & Engn, Shenzhen 518172, Guangdong, Peoples R China

[4] Zhejiang Sci Tech Univ, Dept Math, Hangzhou 310018, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2020年 / 156卷

基金：

中国国家自然科学基金;

关键词：

Nonlinear Schrodinger equation; Three-level linearized difference scheme; Artificial boundary condition; Stability; Convergence; ADI METHOD; DOMAIN;

D O I：

10.1016/j.apnum.2020.04.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 secondorder accuracy both in time and space. Finally, several numerical examples are given to verify the theoretical results. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：32 / 49

页数：18

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