Abstract We consider a generic type of nonlinear Hammerstein-type integral equations with the particularity having non-differentiable kernel Nemystkii type. So, in order to solve it we uniparametric family iterative processes derivative free, main advantage that for special value involved parameter method obtained coincides Newton’s method, is due fact evaluating divided difference operator whe...

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...

in this article,we present a wavelet method for solving stochastic volterra integral equations based on haar wavelets. first, we approximate all functions involved in the problem by haar wavelets then, by substituting the obtained approximations in the problem, using the it^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...

A numerical method for finding the solution of nonlinear VolterraHammerstein integral equations is proposed. The properties of the hybrid functions which consists of block-pulse functions plus rationalized Haar functions are presented. The hybrid functions together with the operational matrices of integration and product are then utilized to reduce the solution of nonlinear Volterra-Hammerstein...

alternative legendre polynomials (alps) are used to approximate the solution of a class of nonlinear volterra-hammerstein integral equations. for this purpose, the operational matrices of integration and the product for alps are derived. then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. the error analysis of the method is given an...