in this paper, a nonlinear volterra-fredholm integral equation of the first kind is solved by using the homotopy analysis method (ham). in this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by ham. the approximate solution of this equation is calculated in the form of a series which its components are computed easily. the accuracy...

in this paper, we present a numerical method for solving nonlinear fredholm and volterra integral equations of the second kind which is based on the use of haar wavelets and collocation method. we use properties of block pulse functions (bpf) for solving volterra integral equation. numerical examples show efficiency of the method.

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 effc...

A numerical method for solving nonlinear Fredholm-Volterra integral equations is presented. The method is based upon Lagrange functions approximations. These functions together with the Gaussian quadrature rule are then utilized to reduce the Fredholm-Volterra integral equations to the solution of algebraic equations. Some examples are included to demonstrate the validity and applicability of t...

Abstract A new numerical method based on Haar wavelet is proposed for two-dimensional nonlinear Fredholm, Volterra and Volterra-Fredholm integral equations of first and second kind. The proposed method is an extension of the Haar wavelet method [1–3] from one-dimensional nonlinear integral equations (Fredholm and Volterra) to twodimensional nonlinear integral equations (Fredholm, Volterra and V...

In this paper, we apply the local fractional Adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of Fredholm integral equations of the second kind within local fractional derivative operators. The iteration procedure is based on local fractional derivative. The obtained results reveal that the proposed methods are very efficient and simple tools ...

In this article the nonlinear mixed Volterra-Fredholm integral equations are investigated by means of the modified threedimensional block-pulse functions (M3D-BFs). This method converts the nonlinear mixed Volterra-Fredholm integral equations into a nonlinear system of algebraic equations. The illustrative examples are provided to demonstrate the applicability and simplicity of our scheme.

I n recent years, many numerical methods have been proposed for solving fuzzy linear integral equations. For example, in [10], the authors used the divided differences and finite differences methods for solving a parametric of the fuzzy Fredholm integral equations of the second kind. Also, in [9], a numerical method is proposed for the approximate solution of fuzzy linear Fredholm functional in...

The well-known Kantorovich technique based on majorizing sequences is used to analyse the convergence of Newton’s method when it is used to solve nonlinear Fredholm integral equations. In addition, we obtain information about the domains of existence and uniqueness of a solution for these equations. Finally, we illustrate the above with two particular Fredholm integral equations.

In this paper, we use the parametric form of fuzzy numbers, and aniterative approach for obtaining approximate solution for a classof fuzzy nonlinear Fredholm integral equations of the second kindis proposed. This paper presents a method based on Newton-Cotesmethods with positive coefficient. Then we obtain approximatesolution of the fuzzy nonlinear integral equations by an iterativeapproach.