On the numerical solution of nonlinear Hammerstein integral equations using Legendre approximation

Abstract

In this study, Legendre collocation method is presented to solve numerically the Fredholm-Hammerstein integral equations. This method is based on replacement of the unknown function bytruncated series of well known Legendre expansion of functions. The proposed method converts theequation to matrix equation, by means of collocation points on the interval [?1, 1] which correspondingto system of algebraic equations with Legendre coefficients. Thus, by solving the matrix equation,Legendre coefficients are obtained. Some numerical examples are included to demonstrate the validityand applicability of the proposed technique