带波动算子的非线性薛定谔方程的人工边界条件  

ARTIFICIAL BOUNDARY CONDITIONS OF THE NONLINEAR SCHRDINGER EQUATION WITH WAVE OPERATOR ON UNBOUNDED DOMAINS

作　　者：赵鑫 胡云霞 李宏伟 Zhao Xin;Hu Yunxia;Li Hongwei(School of Mathematics and Statistics,Shandong Normal University,250358,Jinan,China)

机构地区：[1]山东师范大学数学与统计学院,济南250358

出　　处：《山东师范大学学报（自然科学版）》2018年第4期388-395,共8页Journal of Shandong Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11401350)

摘　　要：本文研究带波动算子的非线性薛定谔方程在无界区域上的数值解.在无界区域上引入人工边界,基于算子分裂方法的统一方法在人工边界上构造合理的人工边界条件,将无界区域上的原问题简化为有界计算区域上的初边值问题,利用有限差分方法进行数值离散.构造质量泛函分析了简化初边值问题的稳定性.最后,通过数值算例验证方法的有效性.The numerical solution of the nonlinear Schr,dinger equation with wave operator on unbounded domain is considered in this paper.Based on the artificial boundary method and the idea of the operator splitting method,local absorbing boundary conditions are designed to reduce the nonlinear problem on unbounded domain to an initial boundary value problem on a bounded domain,which can be solved by the finite difference method.The stability analysis of the reduced problem is given by the construction of mass function.Finally,numerical results are given to demonstrate the effectiveness of the proposed method.

关 键 词：带波动算子的非线性薛定谔方程 无界区域 人工边界方法 稳定性 

分 类 号：O241.82[理学—计算数学]