Since various problems in science and engineering fields can be modeled by nonlinear Volterra-Fredholm integral equations, the main focus of this study is to present an effective numerical method for solving them. This method is based on the hybrid functions of Legendre polynomials and block-pulse functions. By using this approach, a nonlinear Volterra-Fredholm integral equation reduces to a no...

We consider nonlinear integral equations of Fredholm and Volterra type with respect to functions having values in L-spaces. Such class of equations includes set-valued integral equations, fuzzy integral equations and many others. We prove theorems of existence and uniqueness of the solutions for such equations and investigate data dependence of their solutions.

A general class of convergent methods for the numerical solution of ordinary differential equations is employed to obtain a class of convergent generalized reducible quadrature methods for Volterra integral equations of the second kind and Volterra integro-differential equations.

In this paper, a numerical method for solving the Fredholm and Volterra integral equations is presented. The method is based upon the second Chebyshev wavelet approximation. The properties of the second Chebyshev wavelet are first presented and then operational matrix of integration of the second Chebyshev wavelets basis and product operation matrix of it are derived. The second Chebyshev wavel...

stefan problem with kinetics is reduced to a system of nonlinear volterra integral equations of second kind and newton's method is applied to linearize it. product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. an example is provided to illustrated the applicability of the method.

Abstract In this paper, we study the Legendre wavelets for the solution of linear, nonlinear and singular Fredholm integral equations of second kind using approximation technique. The properties of Legendre wavelets together with the Gaussian integration method are used to reduce the problem to the solution of algebraic equations. The main purpose of this article is to discuss the theoretical a...

This article proposes a fast and accurate expansion-iterative method for solving second kind linear Volterra integral equations. The method is based on a special representation of vector forms of triangular functions (TFs) and their operational matrix of integration. By using this approach, solving the integral equation reduces to solve a recurrence relation. The approximate solution of integra...

in this paper, we apply the local fractional laplace transform method (or yang-laplace transform) on volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. the iteration procedure is based on local fractional derivative operators. this approach provides us with a convenient way to find a solution ...