[1]张瑰,张梅,方涵先,等.一类Schrdinger方程的反问题及其变分同化方法[J].南京师大学报(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 Schrdinger Equations[J].Journal of Nanjing Normal University(Natural Science Edition),2012,35(02):24-28.
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一类Schrdinger方程的反问题及其变分同化方法(
)
《南京师大学报(自然科学版)》[ISSN:1001-4616/CN:32-1239/N]
- 卷:
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第35卷
- 期数:
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2012年02期
- 页码:
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24-28
- 栏目:
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数学
- 出版日期:
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2012-06-20
文章信息/Info
- Title:
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The Variational Assimilation Method of Inverse Problem for a Class of Schrdinger Equations
- 作者:
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张瑰1; 张梅2; 方涵先3; 刘希强1
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( 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):
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Zhang Gui1; Zhang Mei2; Fang Hanxian3; Liu Xiqiang1
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1.Institute of Science,PLA University of Science and Technology,Nanjing 211101,China
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- 关键词:
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Schrdinger 方程; 反问题; 变分同化; 迭代
- Keywords:
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Schrdinger equation; inverse problem; variational assimilation; iterative
- 分类号:
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O241.6
- 摘要:
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主要讨论一类Schrdinger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:
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The inverse problem of Schrdinger 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 Schrdinger 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 Schrdinger equation in Hs[J]. Nonlinear Analysis, TMA,1990,14: 807-836.
[2] Wang Baoxiang. On the initial-boundary value problems for nonlinear Schrdinger 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 Schrdinger 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:
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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