In this article, we study the exact controllability of an abstract model described by the controlled generalized Hammerstein type integral equation

We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein-type Volterra integral equations (VIEs) whose solutions may blow up in finite time. To approximate such solutions (and the corresponding blow-up time), we will introduce an adaptive stepsize strategy that guarantees the existence of collocation solutions whose blow-up behavior is the same as the one for the e...

The numerical solutions to the nonlinear integral equations of Hammerstein-type y(t) =f(t) + 11 k(t,s)g(s,y(s))ds, t E [0,1] with using Daubechies wavelets are investigated. A general kernel scheme basing on Daubechies wavelets combined with a collocation method is presented. The approach of creating Daubechies interval wavelets and their main properties are briefly mentioned. Also we present a...

In this paper, we show that the residual can be used to estimate the error of a numerical solution for a class of nonlinear Hammerstein equations. It is also shown that the superconvergence of the iterated numerical solution provides a sufficient condition for the residual to be used as an error estimator. Hammerstein equations with smooth as well as wekly singular kernels will be treated.

Analytical solutions of integral equations, either do not exist or are hard to find. Due to this, many numerical methods have been developed for finding the solutions of integral equations. The use of wavelets has come to prominence during the last two decades. Wavelets can be used as analytical tools for signal processing, numerical analysis and mathematical modeling. The early works concernin...