Articles

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

  • Yunxia WEI ,
  • Yanping CHEN
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  • 1. Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, China;
    2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
Yunxia WEI,E-mail:yunxiawei@126.com

Received date: 2016-01-28

  Revised date: 2016-12-29

  Online published: 2017-08-25

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).

Abstract

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.

Cite this article

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 . DOI: 10.1016/S0252-9602(17)30060-7

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