Recent papers, , & , describe some algorithms for linear first kind integral equations. These algorithms are based on augmented Galerkin method and Cross-validation scheme . The results show that, these algorithms work well for linear equations. In this paper we apply algorithms of  &  on non-linear first kind integral equations of Hammerstein type with bounded solution. In order to obtain a posteriori error estimate, we apply fifteen-point Gauss-Kronrod quadrature rule . Finally, we give a number of numerical examples showing that the algorithms work well in practice.
Available at: http://works.bepress.com/saeid_abbasbandy/5/