Sinc-collocation methods for weakly singular Fredholm integral equations of the second kind

被引：59

作者：

Okayama, Tomoaki ^{[1
]}

Matsuo, Takayasu ^{[1
]}

Sugihara, Masaaki ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Informat Sci & Technol, Bunkyo Ku, Tokyo 1138656, Japan

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2010年 / 234卷 / 04期

关键词：

Fredholm integral equation; Weakly singular kernel; Sinc approximation; Smoothing transformation; NUMERICAL-SOLUTION; PRODUCT INTEGRATION; KERNELS; TRANSFORMATION; APPROXIMATION;

D O I：

10.1016/j.cam.2009.07.049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we propose new numerical methods for linear Fredholm integral equations of the second kind with weakly singular kernels. The methods are developed by means of the Sinc approximation with smoothing transformations, which is an effective technique against the singularities of the equations. Numerical examples show that the methods achieve exponential convergence, and in this sense the methods improve conventional results where only polynomial convergence have been reported so far. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：1211 / 1227

页数：17

共 25 条

[1]

Atkinson KE., 1996, Cambridge Monographs on Applied and Computational Mathematics

[2] A new approach to the numerical solution of weakly singular Volterra integral equations [J].

Baratella, P ;

Orsi, AP .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 163 (02) :401-418

[3] A note on the convergence of product integration and Galerkin method for weakly singular integral equations [J].

Baratella, P .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1997, 85 (01) :11-18

[4]

Brunner, 2010, 7 LECTIRES THEORY NU

[5] Variable transformations in the numerical solution of second kind Volterra integral equations with continuous and weakly singular kernels; extensions to Fredholm integral equations [J].

Galperin, EA ;

Kansa, EJ ;

Makroglou, A ;

Nelson, SA .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 115 (1-2) :193-211

[6]

GRAHAM IG, 1982, MATH COMPUT, V39, P519, DOI 10.1090/S0025-5718-1982-0669644-3

[7]

GRAHAM IG, 1982, J INTEGRAL EQUAT, V4, P1

[8]

Kythe PK., 2011, Computational Methods for Linear Integral Equations

[9] High order methods for weakly singular integral equations with nonsmooth input functions [J].

Monegato, G ;

Scuderi, L .

MATHEMATICS OF COMPUTATION, 1998, 67 (224) :1493-1515

[10] The double-exponential transformation in numerical analysis [J].

Mori, M ;

Sugihara, M .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 127 (1-2) :287-296

← 1 2 3 →