On the Numerical Solution of Hammerstein Integral Equations using Legendre Approximation

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 by truncated series of well known Legendre expansion of functions. The proposed method converts the equation to matrix equation, by means of collocation points on the interval [i1;1] which corresponding to system of algebraic equations with Legendre coe‐cients. Thus, by solving the matrix equation, Legendre coe‐cients are obtained. Some numerical examples are included to demonstrate the validity and applicability of the proposed technique.