Legendre spectral collocation method for volterra-hammerstein integral equation of the second kind

This paper is concerned with obtaining theapproximate solution for Volterra-Hammerstein 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.