LEGENDRE SPECTRAL COLLOCATION METHOD FOR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION OF THE SECOND KIND

doi:10.1016/S0252-9602(17)30060-7

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (4): 1105-1114.doi: 10.1016/S0252-9602(17)30060-7

LEGENDRE SPECTRAL COLLOCATION METHOD FOR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION OF THE SECOND KIND

魏云霞¹, 陈艳萍²

1. Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, China;
2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

收稿日期:2016-01-28 修回日期:2016-12-29 出版日期:2017-08-25 发布日期:2017-08-25
通讯作者: Yanping CHEN,E-mail:yanpingchen@scnu.edu.cn E-mail:yanpingchen@scnu.edu.cn
作者简介:Yunxia WEI,E-mail:yunxiawei@126.com
基金资助:
This work was supported by National Natural Science Foundation of China (11401347, 91430104, 11671157, 61401255, 11426193) and Shandong Province Natural Science Foundation (ZR2014AP003).

LEGENDRE SPECTRAL COLLOCATION METHOD FOR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION OF THE SECOND KIND

Yunxia WEI¹, Yanping CHEN²

1. Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, China;
2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

Received:2016-01-28 Revised:2016-12-29 Online:2017-08-25 Published:2017-08-25
Contact: Yanping CHEN,E-mail:yanpingchen@scnu.edu.cn E-mail:yanpingchen@scnu.edu.cn
About author:Yunxia WEI,E-mail:yunxiawei@126.com
Supported by:
This work was supported by National Natural Science Foundation of China (11401347, 91430104, 11671157, 61401255, 11426193) and Shandong Province Natural Science Foundation (ZR2014AP003).

摘要/Abstract

摘要：

This paper is concerned with obtaining the approximate solution for VolterraHammerstein integral equation with a regular kernel. We choose the Gauss points associated with the Legendre weight function ω(x)=1 as the collocation points. The Legendre collocation discretization is proposed for Volterra-Hammerstein integral equation. We provide an error analysis which justifies that the errors of approximate solution decay exponentially in L² norm and L^∞ norm. We give two numerical examples in order to illustrate the validity of the proposed Legendre spectral collocation method.

关键词: Volterra-Hammerstein integral equation, Legendre collocation discretization, Gauss quadrature formula

Abstract:

Key words: Volterra-Hammerstein integral equation, Legendre collocation discretization, Gauss quadrature formula

魏云霞, 陈艳萍. LEGENDRE SPECTRAL COLLOCATION METHOD FOR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION OF THE SECOND KIND[J]. 数学物理学报(英文版), 2017, 37(4): 1105-1114.

Yunxia WEI, Yanping CHEN. LEGENDRE SPECTRAL COLLOCATION METHOD FOR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION OF THE SECOND KIND[J]. Acta mathematica scientia,Series B, 2017, 37(4): 1105-1114.

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LEGENDRE SPECTRAL COLLOCATION METHOD FOR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION OF THE SECOND KIND

LEGENDRE SPECTRAL COLLOCATION METHOD FOR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION OF THE SECOND KIND

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