This paper aims to prove that the solution of the integral equation systems exists via the
concepts of fixed point and multi-valued operators. For this purpose, at first, some new …

In this paper, a new general form for the non-polynomial cubic spline function is introduced.
This form enables us to generate about ten different formulas of the proposed spline …

In this paper, a new numerical iterative method based on the successive approximations
method for solving nonlinear Hammerstein Volterra integral equations of the second kind is …

In this paper, the numerical solution of nonlinear Fredholm integral equations of the second
kind is considered by two methods. The methods are developed by means of the Sinc …

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterra
integral equations, using the globally defined B-spline and auxiliary basis functions. The …

In our knowledge so far, the Non-polynomial Spline functions (NPS) have not been yet
applied for approximating the integral equations. In this article, we want to use such …

In this paper, we want to exemplify the use of extrapolation methods (namely, Shanks
transformations, the recursive algorithms for their implementation, and the freely available …

This paper deals with convolution-type Urysohn equations of the first kind. Finding a solution
for such equations is an ill-posed problem. For it to be solved, regularization algorithms and …

For this work, the main idea is to make an adapted modification to the Newton-Kantorovich
method destined to solve a nonlinear integral equations, so that by this technical method we …

In this study, we propose a highly accurate technique for solving Volterra and Fredholm
integral equations based on the blending of the Chebyshev pseudo methods. The …