关于求解非线性耦合Schrodinger 方程的 Sonnier - Christov 格式

数学物理学报 ›› 2010, Vol. 30 ›› Issue (1): 114-125.

关于求解非线性耦合Schrodinger 方程的 Sonnier - Christov 格式

王廷春, 张鲁明, 陈芳启

1.南京航空航天大学理学院南京 210016；2.北京应用物理与计算数学研究所北京 100088

收稿日期:2007-12-15 修回日期:2009-02-16 出版日期:2010-01-01 发布日期:2010-01-01
基金资助:
国家自然科学基金(10572057)资助.

On Sonnier-Christov's Difference Scheme for the Nonlinear Coupled Schrodinger System

WANG Ting-Chun, ZHANG Lu-Ming, CHEN Fang-Qi

1.College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016；2.Institute of Applied Physics and Computational Mathematics, Beijing 100088

Received:2007-12-15 Revised:2009-02-16 Online:2010-01-01 Published:2010-01-01
Supported by:
国家自然科学基金(10572057)资助.

摘要/Abstract

摘要：

该文对求解非线性耦合Schrodinger方程的Sonnier-Christov格式进行了数值分析, 证明了格式关于L₂范数的稳定性和二阶收敛性, 运用Brouwer不动点定理证明了差分解的存在唯一性, 给出一个求解非线性差分方程组的迭代算法并证明了算法的收敛性, 最后对双孤立波的碰撞进行了模拟.

关键词: 非线性耦合Schrodinger方程, Sonnier-Christov格式, 可解性, 稳定性, 收敛性, 迭代算法

Abstract:

In this paper, numerical analysis of the Sonnier-Christov's difference scheme for the coupled nonlinear Schrodinger system is given. we prove that the difference scheme is unconditional stable and the second-order convergent in discrete L₂-norm. Unique existence of the numerical solution and a iterative algorithm are also discussed in detail. Collision of two solitary waves is also simulated.

中图分类号:

60M06

王廷春, 张鲁明, 陈芳启. 关于求解非线性耦合Schrodinger 方程的 Sonnier - Christov 格式[J]. 数学物理学报, 2010, 30(1): 114-125.

WANG Ting-Chun, ZHANG Lu-Ming, CHEN Fang-Qi. On Sonnier-Christov's Difference Scheme for the Nonlinear Coupled Schrodinger System [J]. Acta mathematica scientia,Series A, 2010, 30(1): 114-125.

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