Hybrid collocation methods for Fredholm integral equations with weakly singular kernels

被引：45

作者：

Cao, Yanzhao

Huang, Min

Liu, Liping

Xu, Yuesheng ^{[1
]}

机构：

[1] Syracuse Univ, Dept Math, Syracuse, NY 13244 USA

[2] Florida A&M Univ, Dept Math, Tallahassee, FL 32307 USA

[3] Lakehead Univ, Dept Math Sci, Thunder Bay, ON P7B 5E1, Canada

来源：

APPLIED NUMERICAL MATHEMATICS | 2007年 / 57卷 / 5-7期

基金：

美国国家科学基金会; 中国国家自然科学基金; 加拿大自然科学与工程研究理事会;

关键词：

Fredholm integral equations; Fredholm integro-differential equations; hybrid collocation methods;

D O I：

10.1016/j.apnum.2006.07.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A hybrid collocation method for Volterra integral equations with weakly singular kernels was developed in [Y. Cao, T. Herdman, Y. Xu, A hybrid collocation method for Volterra integral equations with weakly singular kernels, SIAM J. Numer. Anal. 41 (2003) 364-381. [5]]. The main purpose of this paper is to study the numerical solution of Fredholm integral equations of the second kind with weakly singular kernels by using the hybrid collocation method. The optimal order of convergence for this method for Fredholm integral equations is proved. We also apply the hybrid collocation method to Fredholm integro-differential equations. The superconvergence property of the iteration of the hybrid collocation solution is established. Numerical examples are presented to confirm the theoretical results. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：549 / 561

页数：13

共 49 条

[1] 2-GRID ITERATION METHODS FOR LINEAR INTEGRAL-EQUATIONS OF THE 2ND KIND ON PIECEWISE-SMOOTH SURFACES IN R3 [J].