Numerical solutions for Fredholm integral equations of the second kind with weakly singular kernel using spectral collocation method

被引：16

作者：

Yang, Yin ^{[1
]}

Tang, Zhuyan ^{[1
]}

Huang, Yunqing ^{[1
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Key Lab Intelligent Comp & Informat Proc,Minist E, Xiangtan 411105, Hunan, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2019年 / 349卷

关键词：

Spectral collocation method; Jacobi polynomial; Fredholm integral equations; Singular kernels; CONVERGENCE ANALYSIS; LAGRANGE INTERPOLATION; GALERKIN METHODS;

D O I：

10.1016/j.amc.2018.12.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the spectral collocation for Fredholm integral equations of the second kind with weakly singular kernel. The Jacobi-Gauss quadrature formula is used to approximate the integral operator in the numerical implementation. We obtain the convergence rates for the approximated solution of weakly singular Fredholm integral equations, which show that the errors of the approximate solution decay exponentially in L-infinity-norm and weighted L-2-norm. Some numerical examples are given to illustrate the theoretical results. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：314 / 324

页数：11

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