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| 基于小波的带Hilbert核的奇异积分方程的解法 | |
| 引用本文： | 崔丽敏,王义龙,廖福成,冯象初,唐远炎.基于小波的带Hilbert核的奇异积分方程的解法[J].北京科技大学学报,2005,27(6):764-768. |
| 作者姓名： | 崔丽敏 王义龙 廖福成 冯象初 唐远炎 |
| 作者单位： | 1. 北京科技大学数力系,北京,100083 2. 西安电子科技大学理学院,西安,710071 3. 香港浸会大学计算机科学系,香港 |
| 摘 要： | 许多力学和工程问题都可以表示为第一类奇异积分方程.本文给出了带Hilbert核的奇异积分方程的小波Galerkin算法.利用L2(0,1])上的周期小波和Hilbert核的特点降低刚性矩阵的维数;并且通过阈值使得矩阵更加稀疏,以减少计算量和节省存储空间.根据Hilbert核的奇异性,通过Tikhonov正则化方法求解了所得到的刚性方程组,给出了算法的收敛性和数值结果. |
| 关 键 词： | 周期小波 Galerkin方法 Tikhonov正则化方法 奇异积分方程 周期小波 Hilbert kernel 奇异积分方程 解法 wavelet based singular integral equation 数值结果 算法的收敛性 刚性方程组 求解 正则化方法 Tikhonov 奇异性 存储空间 计算量 阈值 维数 矩阵 利用 |
| 收稿时间： | 12 1 2004 12:00AM |
| 修稿时间： | 01 17 2005 12:00AM |
Solution for the singular integral equation with Hilbert kernel based on wavelet |
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| CUI Limin,WANG Yilong,LIAO Fucheng,FENG Xiangchu,TANG Yuanyan.Solution for the singular integral equation with Hilbert kernel based on wavelet[J].Journal of University of Science and Technology Beijing,2005,27(6):764-768. | |
| Authors: | CUI Limin WANG Yilong LIAO Fucheng FENG Xiangchu TANG Yuanyan |
| 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 L~2(0,l]) 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. |
| Keywords: | periodic wavelet Galerkin method Tikhonov regularization method singular integral equation |
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