| 第二类Fredholm积分方程的快速数值解法 |
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| 引用本文： | 吴静.第二类Fredholm积分方程的快速数值解法[J].广东轻工职业技术学院学报,2004,3(1):1-5. |
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| 作者姓名： | 吴静 |
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| 作者单位： | 广东轻工职业技术学院,基础部,广东,广州,510300 |
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| 摘 要： | 对于具有弱奇性核函数的第二类Fredholm积分方程，将核函数所定义的区域分成大小不同的正方形子区域，利用分层插值多项式逼近核函数，由此得到近似矩阵B实现了积分方程的快速数值解法。在最后，对如何提高方案的数值稳定性作简要讨论并给出要讨论并给出数值结果。
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| 关 键 词： | Fredholm积分方程 插值多项式 广义极小剩余法 弱奇性核函数 快速数值解法 |
| 文章编号： | 1672-1950（2004）01-0001-05 |
| 收稿时间： | 2004-01-26 |
| 修稿时间： | 2004年1月26日 |
Fast Algorithm of the Second Fredholm Equations with Weakly Singular Kernels |
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| Wu Jing.Fast Algorithm of the Second Fredholm Equations with Weakly Singular Kernels[J].Journal of Guangdong Industry Technical College,2004,3(1):1-5. |
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| Authors: | Wu Jing |
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| Institution: | Department of Elementary Courses,Guangdong Industry Technical College, Guangzhou 510300, China. |
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| Abstract: | In this paper, the author considers solutions of Fredholm integral equations of the second kind where the kernel functions are weakly singular. They present a scheme based on polynomial interpolation to approximate the discretlzation matrix of the integral operator. Their approximation matrix B is obtained by partitioning the domain in which the kernel function is defined into subdomains of different size and approximating the kernel function at each subdomain by interpolating polynomial at equidistance points. They will discuss the stability of the algorithm and numerical. Finally results are given to illustrate the stability and efficiency of the algorithm. |
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| Keywords: | Fredholm integral equation polynomial interpolation GMRES |
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