A new parametric class of iterative schemes for solving nonlinear systems is designed. The third- or fourth-order convergence, depending on the values parameter being proven. analysis dynamical behavior this in context scalar equations presented. This study gives us important information about stability and reliability members family. numerical results obtained by applying different elements fa...

There are various numerical methods to solve nonlinear integral equations. Most of them transform the integral equation into a system of nonlinear algebraic equations. It is cumbersome to solve these systems, or the solution may be unreliable. In this paper, we study the application of the fixed point method to solve Volterra-Hammerstein integral equations. This method does not lead to a nonlin...

In this paper we consider the solutions to two neighbouring Hammerstein-type Volterra integral equations of the form

in this paper‎, ‎existence of an $l^p$-solution for 2dies (two‎ ‎dimensional integral equations) of the hammerstein type is‎ ‎discussed‎. ‎the main tools in this discussion are schaefer's and‎ ‎schauder's fixed point theorems with a general version of‎ ‎gronwall's inequality‎.

In this paper, the well known iterated Galerkin method and iterated Galerkin-Kantorovich regularization method for approximating the solution of Fredholm integral equations of the second kind are generalized to Hammerstein equations with smooth and weakly singular kernels. The order of convergence of the Galerkin method and those of superconvergence of the iterated methods are analyzed. Numeric...