解带有Hilbert核的奇异积分方程的高精度组合算法  

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

作　　者：黄晋[1] 吕涛[2] 朱瑞[2] 

机构地区：[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

出　　处：《数学物理学报（A辑）》2009年第1期103-113,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(10171073)资助

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.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 Bδ, 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.

关 键 词：Hilber奇异积分方程 组合算法 后验误差估计 求积法. 

分 类 号：O241.82[理学—计算数学]