[1]张瑰,张梅,方涵先,等.一类Schrdinger方程的反问题及其变分同化方法[J].南京师范大学学报(自然科学版),2012,35(02):24-28.
 Zhang Gui,Zhang Mei,Fang Hanxian,et al.The Variational Assimilation Method of Inverse Problem for a Class of Schrdinger Equations[J].Journal of Nanjing Normal University(Natural Science Edition),2012,35(02):24-28.
点击复制

一类Schrdinger方程的反问题及其变分同化方法()
分享到:

《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第35卷
期数:
2012年02期
页码:
24-28
栏目:
数学
出版日期:
2012-06-20

文章信息/Info

Title:
The Variational Assimilation Method of Inverse Problem for a Class of Schrdinger Equations
作者:
张瑰1张梅2方涵先3刘希强1
( 1. 解放军理工大学理学院,江苏南京211101) ( 2. 南京农业大学理学院,江苏南京210095) ( 3. 解放军理工大学气象学院,江苏南京211101)
Author(s):
Zhang Gui1Zhang Mei2Fang Hanxian3Liu Xiqiang1
1.Institute of Science,PLA University of Science and Technology,Nanjing 211101,China
关键词:
Schrdinger 方程反问题变分同化迭代
Keywords:
Schrdinger equationinverse problemvariational assimilationiterative
分类号:
O241.6
摘要:
主要讨论一类Schrdinger方程的反问题,利用变分同化方法,给出了最速下降的迭代格式,通过已知的观测值对模式的初值和未知点源进行最优修正.文中不仅给出了反问题的收敛格式,还进行了数值计算,其结果与理论结果吻合.
Abstract:
The inverse problem of Schrdinger equation was considered in this paper. And the fast speed iterative process was given with variational assimilation method. The initial value and unknown point sources of the model were modified with the known observations. An iteration scheme for the inverde problem of the Schrdinger equations was obtained, and the theoretical results were in good agreement with the experimental results.

参考文献/References:

[1] Gazenave T,Weissler F B. The Cauchy problem for critical nonlinear Schrdinger equation in Hs[J]. Nonlinear Analysis, TMA,1990,14: 807-836.
[2] Wang Baoxiang. On the initial-boundary value problems for nonlinear Schrdinger equations[J]. Advances in Mathematics, 2000,29( 5) : 421-424.
[3] Navon I M. Practical and theoretical aspects of adjoint parameter estimation and identifiablity in meteorology and oceanography [J]. Dyn Atmos Oceans,1997,27: 55-79.
[4] 张瑰. 一维扩散方程整体观测资料下的初值变分同化反演[J]. 海洋预报,2006,23( 21) : 34-41.
[5] 张瑰,黄思训. 一类on-off 问题的变分同化方法的误差估计[J]. 工程数学学报,2009,26( 1) : 37-42.
[6] Teng Jiajun,Zhang Gui. Huang Sixun. Some theoretical problems on variational data assimilation[J]. Applied Mathematics and Mechanics,2007,28( 5) : 651-663.
[7] 方涵先,黄思训. 二维下投式探空仪反演的理论分析与数值试验[J]. 自然科学进展,2004,14( 11) : 1 257-1 264.
[8] Zhang Gui,Li Zhenxing,Zhu Shouxian. The error estimates of predicted value of variational assimilation method for a class of Schrdinger equations[C]. Manchester: The Second International Conference on Information and Computing Science, 2009: 304-307.
[9] Huang Sixun,Du Huadong,Han Wei. Generalized variational data assimilation method and numerical experiment for nondifferential system[J]. Appl Math Mech,2004,25( 10) : 1 160-1 165.
[10] 张瑰,张梅. 人口模型变分同化方法的理论分析[J]. 大学数学,2004,20( 5) : 30-33.

备注/Memo

备注/Memo:
基金项目: 国家自然科学基金( 41105012, 40906044) 、解放军理工大学预研基金( 20110510) .
通讯联系人: 张瑰,博士,副教授,研究方向: 数学物理反问题与变分同化方法. E-mail: zhanggui73@163. com
更新日期/Last Update: 2013-03-11