Using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of Hammerstein type . The mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). The procedure of this method is so fast and don't need high cpu and complicated programming. The advantages of this method are that we can applied for those integral equations whi...

degenerate kernel approximation method is generalized to solve hammerstein system of fredholm integral equations of the second kind. this method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. convergence analysis is investigated and on some test problems, the propo...

A numerical method for solving nonlinear mixed Hammerstein integral equations is presented in this paper. The method is based upon hybrid of rationalized Haar functions approximations. The properties of hybrid functions which are the combinations of block-pulse functions and rationalized Haar functions are first presented. The Newton-Cotes nodes and Newton-Cotes integration method are then util...

In this paper the existence of a positive measurable solution of the Hammerstein equation of the first kind with a singular nonlinear term at the origin is presented. 0. Introduction The literature on the Hammerstein equations with the reciprocal of the solution in the integrand is rather limited, although there are many applications. For example, the equation

In this chapter, we survey recent results on the numerical solutions of the Hammerstein equations. Hammerstein equations arise naturally in connection with the Laplace equation with a certain class of nonlinear boundary conditions. The Hammerstein equations with smooth as well as weakly singular kernels will be treated.

We study a class of nonlinear operators that can be written as the composition linear operator and map. obtain results on fixed point index based parameters are related to definitions spectra. As particular case, existence positive solutions for second-order differential equation with separated boundary conditions is proved. The result also provides spectral interval corresponding Hammerstein i...