| Wavelet Numerical Solutions for Weakly Singular Fredholm Integral Equations of the Second Kind |
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| 引用本文： | TANG Xinjian PANG Zhicheng ZHU Tonglin LIU Jian. Wavelet Numerical Solutions for Weakly Singular Fredholm Integral Equations of the Second Kind[J]. 武汉大学学报:自然科学英文版, 2007, 12(3): 437-441. DOI: 10.1007/s11859-006-0110-5 |
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| 作者姓名： | TANG Xinjian PANG Zhicheng ZHU Tonglin LIU Jian |
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| 作者单位： | [1]Institute of Patters Recognition and Artificial Intelligence, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China; [2]Institute of Rock and Soil Mechanics, Chinese Academy of Science, Wuhan 430071, Hubei, China; [3]School of Information, South China Agricultural University, Guangzhou 510642, Guangdong, China |
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| 基金项目： | Supported by the National Natural Science Foundation of China （60572048） and the Natural Science Foundation of Guangdong Province （054006621） |
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| 摘 要： | Daubechies interval wavelet is used to solve numerically weakly singular Fredholm integral equations of the second kind. Utilizing the orthogonality of the wavelet basis,the integral equation is reduced into a linear system of equations. The vanishing moments of the wavelet make the wavelet coefficient matrices sparse,while the continuity of the derivative functions of basis overcomes naturally the singular problem of the integral solution. The uniform convergence of the approximate solution by the wavelet method is proved and the error bound is given. Finally,numerical example is presented to show the application of the wavelet method.
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| 关 键 词： | 弱奇异积分方程 Fredholm积分方程 小波 数值解 |
| 文章编号： | 1007-1202（2007）03-0437-05 |
| 收稿时间： | 2006-11-17 |
| 修稿时间： | 2006-11-17 |
Wavelet numerical solutions for weakly singular Fredholm integral equations of the second kind |
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| Tang Xinjian,Pang Zhicheng,Zhu Tonglin,Liu Jian. Wavelet numerical solutions for weakly singular Fredholm integral equations of the second kind[J]. Wuhan University Journal of Natural Sciences, 2007, 12(3): 437-441. DOI: 10.1007/s11859-006-0110-5 |
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| Authors: | Tang Xinjian Pang Zhicheng Zhu Tonglin Liu Jian |
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| Affiliation: | (1) Institute of Patters Recognition and Artificial Intelligence, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China;(2) Institute of Rock and Soil Mechanics, Chinese Academy of Science, Wuhan, 430071, Hubei, China;(3) School of Information, South China Agricultural University, Guangzhou, 510642, Guangdong, China |
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| Abstract: | Daubechies interval cally weakly singular Fredholm kind. Utilizing the orthogonality equation is reduced into a linear wavelet is used to solve nurneriintegral equations of the second of the wavelet basis, the integral system of equations. The vanishing moments of the wavelet make the wavelet coefficient matrices sparse, while the continuity of the derivative functions of basis overcomes naturally the singular problem of the integral solution. The uniform convergence of the approximate solution by the wavelet method is proved and the error bound is given. Finally, numerical example is presented to show the application of the wavelet method. |
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| Keywords: | weakly singular integral equations interval wavelet sparse matrix |
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