基于小波的帶Hilbert核的奇異積分方程的解法

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基于小波的帶Hilbert核的奇異積分方程的解法

崔麗敏, 王義龍, 廖福成, 馮象初, 唐遠炎

文章導航 > 工程科學學報 > 2005 > 27(6): 764-768

崔麗敏, 王義龍, 廖福成, 馮象初, 唐遠炎. 基于小波的帶Hilbert核的奇異積分方程的解法[J]. 工程科學學報, 2005, 27(6): 764-768. doi: 10.13374/j.issn1001-053x.2005.06.030

引用本文:

崔麗敏, 王義龍, 廖福成, 馮象初, 唐遠炎. 基于小波的帶Hilbert核的奇異積分方程的解法[J]. 工程科學學報, 2005, 27(6): 764-768. doi: 10.13374/j.issn1001-053x.2005.06.030

CUI Limin, WANG Yilong, LIAO Fucheng, FENG Xiangchu, TANG Yuanyan. Solution for the singular integral equation with Hilbert Kernel based on wavelet[J]. Chinese Journal of Engineering, 2005, 27(6): 764-768. doi: 10.13374/j.issn1001-053x.2005.06.030

Citation:

CUI Limin, WANG Yilong, LIAO Fucheng, FENG Xiangchu, TANG Yuanyan. Solution for the singular integral equation with Hilbert Kernel based on wavelet[J]. Chinese Journal of Engineering, 2005, 27(6): 764-768. doi: 10.13374/j.issn1001-053x.2005.06.030

崔麗敏, 王義龍, 廖福成, 馮象初, 唐遠炎. 基于小波的帶Hilbert核的奇異積分方程的解法[J]. 工程科學學報, 2005, 27(6): 764-768. doi: 10.13374/j.issn1001-053x.2005.06.030

引用本文:

崔麗敏, 王義龍, 廖福成, 馮象初, 唐遠炎. 基于小波的帶Hilbert核的奇異積分方程的解法[J]. 工程科學學報, 2005, 27(6): 764-768. doi: 10.13374/j.issn1001-053x.2005.06.030

CUI Limin, WANG Yilong, LIAO Fucheng, FENG Xiangchu, TANG Yuanyan. Solution for the singular integral equation with Hilbert Kernel based on wavelet[J]. Chinese Journal of Engineering, 2005, 27(6): 764-768. doi: 10.13374/j.issn1001-053x.2005.06.030

Citation:

CUI Limin, WANG Yilong, LIAO Fucheng, FENG Xiangchu, TANG Yuanyan. Solution for the singular integral equation with Hilbert Kernel based on wavelet[J]. Chinese Journal of Engineering, 2005, 27(6): 764-768. doi: 10.13374/j.issn1001-053x.2005.06.030

基于小波的帶Hilbert核的奇異積分方程的解法

doi: 10.13374/j.issn1001-053x.2005.06.030

1. 北京科技大學數力系, 北京 100083;
2. 西安電子科技大學理學院, 西安 710071;
3. 香港浸會大學計算機科學系, 香港

基金項目:

國家自然科學基金（No.90304007）

作者簡介:
崔麗敏(1977-),女,博士研究生

中圖分類號: O241.83
計量
- 文章訪問數: 139
- HTML全文瀏覽量: 31
- PDF下載量: 6
- 被引次數: 0
出版歷程
- 收稿日期: 2004-12-01
- 修回日期: 2005-01-17
- 網絡出版日期: 2021-08-17

Solution for the singular integral equation with Hilbert Kernel based on wavelet

1. Department of Mathematics and Mechanics, University of Science and Technology Beijng, Beijing 100083, China;
2. School of Science, Xidian University, Xi'an 710071, China;
3. Department of Computer Science, Hong Kong Baptist University, Kpwoon Tong, Hong Kon

摘要: 許多力學和工程問題都可以表示為第一類奇異積分方程.本文給出了帶Hilbert核的奇異積分方程的小波Galerkin算法.利用L²([0,1])上的周期小波和Hilbert核的特點降低剛性矩陣的維數;并且通過閾值使得矩陣更加稀疏,以減少計算量和節省存儲空間.根據Hilbert核的奇異性,通過Tikhonov正則化方法求解了所得到的剛性方程組,給出了算法的收斂性和數值結果.
- 周期小波 /
- Galerkin方法 /
- Tikhonov正則化方法 /
- 奇異積分方程
Abstract: Many problems arising in mechanics and technology can be formulated as the first kind of singular integral equation. A Wavelet-Galerkin algorithm for solving the first kind of singular integral equation with Hilbert kernel was presented. In the algorithm the characteristic of periodic wavelet on L²([0,1]) and the Hilbert kernel were used to solve and make the stiff matrix lower dimension and become sparser through threshold. The computational amount was decreased and the memory space was saved. Because of the singularity of Hilbert kernel the Tikhonov regularization method was used to solve the stiff equation system. The convergence and the numerical result of approximate solution are discussed.
- periodic wavelet /
- Galerkin method /
- Tikhonov regularization method /
- singular integral equation

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文章訪問數: 139
HTML全文瀏覽量: 31
PDF下載量: 6
被引次數: 0

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