The finite difference scheme for nonlinear Schrodinger equations on unbounded domain by artificial boundary conditions

被引：13

作者：

Wang, Bo ^{[1
]}

Liang, Dong ^{[2
,3
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

[2] York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada

[3] Ocean Univ China, Sch Math Sci, Qingdao 266100, Shandong, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2018年 / 128卷

基金：

中国国家自然科学基金; 加拿大自然科学与工程研究理事会;

关键词：

Nonlinear Schrodinger equation; Finite difference method; Artificial boundary conditions; Stability; Convergence; NUMERICAL-SOLUTION; INFINITE DOMAIN; CONVERGENCE; STABILITY; WAVES;

D O I：

10.1016/j.apnum.2018.02.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose and analyze a finite difference method for the nonlinear Schrodinger equations on unbounded domain by using artificial boundary conditions. Two artificial boundary conditions are introduced to restrict the original Schrodinger equations on an unbounded domain into an initial-boundary value problem with a bounded domain. Then, a finite difference scheme for the reduced problem is proposed. The important feature of the proposed scheme is that an extrapolation operator is introduced to treat the nonlinear term while the scheme keeps unconditionally stable and does not introduce any oscillations at the artificial boundaries. The proposed scheme with the discrete artificial boundary conditions is rigorously analyzed to yield the unconditional stability and the scheme is also proved to be convergent. Numerical examples are given to show the performance of our scheme. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：183 / 204

页数：22

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