Compactly supported linear semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, an...

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...

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 paper, efficient numerical techniques have been proposed to solve nonlinear Hammerstein fuzzy integral equations. The proposed methods are based on Bernstein polynomials and Legendre wavelets approximation. Usually, nonlinear fuzzy integral equations are very difficult to solve both analytically and numerically. The present methods applied to the integral equations is reduced to solve t...

We study the numerical solvability of a class of nonlinear weakly singular integral equations of Volterra-Hammerstein type with noncompact kernels. We obtain existence and uniqueness results and analyze the product integration methods for these equations under some verifiable conditions on the kernels and nonlinear functions. The convergence analysis is investigated and finally numerical experi...

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...

We are concerning with a nonlinear Hammerstein quadratic integral equation. We prove the existence of at least one positive solution x ∈ L1 under Carathèodory condition. Secondly we will make a link between Peano condition and Carathèodory condition to prove the existence of at least one positive continuous solution. Finally the existence of the maximal and minimal solutions will be proved.