Abstract: In this paper, we present a computational method for solving Fredholm-Hammerstein integral equations of the second kind. The method utilizes CAS wavelets constructed on the unit interval as basis in the Galerkin method and reduces the solution of the Hammerstein integral equation to the solution of a nonlinear system of algebraic equations. Error analysis is presented for this method....

In this paper‎, ‎existence of an $L^p$-solution for 2DIEs (Two‎ ‎Dimensional Integral Equations) of the Hammerstein type is‎ ‎discussed‎. ‎The main tools in this discussion are Schaefer's and‎ ‎Schauder's fixed point theorems with a general version of‎ ‎Gronwall's inequality‎.

Integral equations of mixed Voltera-Fredholm type arise in various physical and biological problems. In the present paper, we obtain the approximate solution of the nonlinear Volterra-Hammerstein integral equations of mixed type in terms of Taylor polynomial. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.

The purpose of this paper is two-fold. First, we develop the Petrov-Galerkin method and the iterated Petrov-Galerkin method for a class of nonlinear Hammerstein equations. Alpert [1] established a class of wavelet basis and applied it to approximate solutions of the Fredholm second kind integral equations by the Galerkin method. He then demonstrated an advantage of a wavelet basis application t...

Let H be a real Hilbert space. For each i = 1, 2, ...m, let Fi, Ki : H → H be bounded and monotone mappings. Assume that the generalized Hammerstein equation u + ∑m i=1 KiFiu = 0 has a solution in H. We construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the generalized Hammerstein equation. Our iterative scheme in this paper seems far simpl...