A new method for solving hypersingular integral equations of the first kind

被引：25
|
作者：
Chen, Zhong [1 ]
Zhou, YongFang [2 ]
机构：
[1] Harbin Inst Tech, Dept Math, Weihai 264209, Shandong, Peoples R China
[2] Heilongjiang Inst Sci & Tech, Dept Math & Mech, Harbin 150027, Hei Long Jiang, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2011年 / 24卷 / 05期
关键词：
Hypersingular integral equations; Reproducing kernel; Exact solution; SCATTERING;
D O I：
10.1016/j.aml.2010.11.028
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A simple and efficient method for solving hypersingular integral equations of the first kind in reproducing kernel spaces is developed. In order to eliminate the singularity of the equation, a transform is used. By improving the traditional reproducing kernel method, which requires the image space of the operator to be W(2)(1) and the operator to be bounded, the exact solutions and the approximate solutions of hypersingular integral equations of the first kind are obtained. The advantage of this numerical method lies in the fact that, on one hand, the approximate solution is continuous, and on the other hand, the approximate solution converges uniformly and rapidly to the exact solution. The validity of the method is illustrated with two examples. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：636 / 641
页数：6
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