解带有Hilbert核的奇异积分方程的高精度组合算法

数学物理学报

解带有Hilbert核的奇异积分方程的高精度组合算法

¹黄晋; ²吕涛; ²朱瑞

(1. 电子科技大学应用数学学院四川成都 610054; 2. 四川大学数学学院四川成都 610064)

收稿日期:2006-04-15 修回日期:2007-09-08 出版日期:2009-02-25 发布日期:2009-02-25
通讯作者: 黄晋
基金资助:
国家自然科学基金(10171073)资助.

High Accuracy Combination Algorithms for Solving Singular Integral Equations with Hilbert Kernel by Quadrature Methods

¹Huang Jin; ²Lü Tao; ²Zhu Rui

(1. College of Applied Mathematics, University of Electronic & Science Technology of China, Sichuan Chengdu 610054; 2. Mathematical College, Sichuan University, Sichuan Chengdu 610064)

Received:2006-04-15 Revised:2007-09-08 Online:2009-02-25 Published:2009-02-25
Contact: Huang Jin

摘要/Abstract

摘要： 该文给出了用求积法解带Hilber核的奇异积分方程的高精度组合算法.把网格点分成互不相交的子集合, 在子集合上并行求解离散方程组, 再利用组合算法求得全局网格点的逼近.如果积分方程的系数属于B_δ, 则求积法的精度可达O(e^-nδ). 此外, 使用组合算法不仅能得到更高的精度阶, 而且能够得到后验误差估计. 数值算例的结果表明组合算法是极其有效的.

关键词: Hilber奇异积分方程, 组合算法, 后验误差估计, 求积法.

Abstract: This paper presents high accuracy combination algorithms for solving singular integral equations with Hilbert kernel by quadrature methods. A given fine grid set is divided into some subsets with different grid points. After these discrete equations dependent on the subsets are solved in parallel, the global fine grid approximations can be computed by the combination algorithms. It shows that the accuracy of quadrature methods is very high with O(e^-nδ) if the coefficients of equations belong to B_δ, Besides, using the combination algorithms can not only obtain a higher order of the accuracy, but also a posterior error estimate is deduced. These excellent numerical results display the significance of these algorithms made in the paper.

Key words: Hilbert singular integral equation, Combination algorithm, A posterior error estimate, Quadrature method.

中图分类号:

65N25

黄晋; 吕涛; 朱瑞. 解带有Hilbert核的奇异积分方程的高精度组合算法[J]. 数学物理学报, 2009, 29(1): 103-113.

Huang Jin; Lü Tao; Zhu Rui. High Accuracy Combination Algorithms for Solving Singular Integral Equations with Hilbert Kernel by Quadrature Methods[J]. Acta mathematica scientia,Series A, 2009, 29(1): 103-113.