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.

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...

We consider a nonlinear Volterra-Fredholm integral equation NVFIE of the second kind. The Volterra kernel is time dependent, and the Fredholm kernel is position dependent. Existence and uniqueness of the solution to this equation, under certain conditions, are discussed. The block-byblock method is introduced to solve such equations numerically. Some numerical examples are given to illustrate o...

Abstract. In this paper, existence and uniqueness theorems for nonlinear fuzzy fractional Fredholm integro-differential equations are investigated. We interpret Fredholm integro-differential equations under fractional generalized Hukuhara derivatives in the Caputo sense, and for this interpretation, we prove existence results in two type of differentiability. Moreover, two examples are given to...

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.

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.

We study the time and temperature dependent correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions 〈ψ(x1, 0)ψ(x2, t)〉±,T . We derive the Fredholm determinant formulae for the correlation functions, by means of the Bethe Ansatz. For the special case x1 = 0, we express correlation functions with Neumann boundary conditions 〈ψ(0, 0)ψ(x2, t)〉+,T , in terms ...

this paper presents a computational method for solving two types of integro-differential equations, system of nonlinear high order volterra-fredholm integro-differential equation(vfides) and nonlinear fractional order integro-differential equations. our tools for this aims is operational matrices of integration and fractional integration. by this method the given problems reduce to solve a syst...

T The nonlinear and linear Volterra-Fredholm ordinary integral equations arise from various physical and biological models. The essential features of these models are of wide applicable. These models provide an important tool for modeling a numerous problems in engineering and science [6, 7]. Modelling of certain physical phenomena and engineering problems [8, 9, 10, 11, 12] leads to two-dimens...