In this work, we give a product Nyström method for solving a Fredholm functional integral equation (FIE) of the second kind. With this method solving FIE reduce to solving an algebraic system of equations. Then we use some theorems to prove the existence and uniqueness of the system. Finally we investigate the convergence of the method.

In this paper, we propose the cubic semi-orthogonal compactly supported B-spline wavelets as a basis functions for the efficient solution of the second kind Fredholm integral equations system. Properties of these wavelets first presented and these properties are then used to reduce the computation of system of integral equations to some algebraic equations. The exponential convergence rate of t...

In this paper, the linear semiorthogonal compactly supported B-spline wavelets together with their dual wavelets have been applied to approximate the solutions of Fredholm integral equations of the second kind. 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 computatio...

In this article we use discrete collocation method for solving Fredholm–Volterra integro– differential equations, because these kinds of integral equations are used in applied sciences and engineering such as models of epidemic diffusion, population dynamics, reaction–diffusion in small cells. Also the above integral equations with convolution kernel will be solved by discrete collocation metho...

Abstract: In this paper, a Sinc-collocation method based on the double exponential transformation for solving Fredholm and Volterra Hammerstein integral equations is presented. Some properties of the Sinc-collocation method required for our subsequent development are given and utilized to reduce the computation of solution of the Hammerstein integral equations to some algebraic equations. Numer...

In the present work, by applying known Bernstein polynomials and their advantageous properties, we establish an efficient iterative algorithm to approximate the numerical solution of fuzzy Fredholm integral equations of the second kind. The convergence of the proposed method is given and the numerical examples illustrate that the proposed iterative algorithm are ‎valid.‎

In this article, we give some results concerning the continuity of the nonlinear Volterra and Fredholm integral operators on the space L1[0,∞). Then by using the concept of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes of nonlinear integral equations. Our results extend some previous works.

In this paper, an iterative scheme for extracting approximate solutions of two dimensional Volterra-Fredholm integral equations is proposed. Considering some conditions on the kernel of the integral equation obtained by discretization of the integral equation, the convergence of the approximate solution to the exact solution is investigated. Several examples are provided to demonstrate the effi...

in this paper, we propose a successive approximation method based on fuzzy wavelet like operator to approximate the solution of linear fuzzy fredholm integral equations of the second kind with arbitrary kernels. we give the convergence conditions and an error estimate. also, we investigate the numerical stability of the computed values with respect to small perturbations in the first iteration....

The first passage time problem for Brownian motions hitting a barrier has been extensively studied in the literature. In particular, many incarnations of integral equations which link the density of the hitting time to the equation for the barrier itself have appeared. Most interestingly, Peskir (2002b) demonstrates that a master integral equation can be used to generate a countable number of n...