In this paper we are going to study the Hyers{Ulam{Rassias typesof stability for nonlinear, nonhomogeneous Volterra integral equations with delayon nite intervals.

The present paper proposes a fast numerical method for the linear Volterra integral equations withregular and weakly singular kernels having smooth solutions. This method is based on the approx-imation of the kernel, to simplify the integral operator and then discretization of the simpliedoperator using a forward dierence formula. To analyze and verify the accuracy of the method, weexamine samp...

In this paper resolvent estimates for Abel integral operators are provided. These estimates are applied to deduce regularizing properties of Lavrentiev's m-times iterated method as well as iterative schemes ? with the discrepancy principle as corresponding parameter choice or stopping rule, respectively for solving the corresponding Abel integral equations of the rst kind.

In this paper, we studied the numerical solution of nonlinear weakly singular Volterra-Fredholm integral equations by using the product integration method. Also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear Volterra-Fredholm integral equations. The reliability and efficiency of the proposed scheme are...

In this paper, we establish some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two independent variables, and we present the applications to research the boundedness of solutions to retarded nonlinear Volterra-Fredholm type integral equations.

In this work we consider a certain class of Volterra integral equations possessing an infinite set of solutions. We investigate the application of Euler’s method together with the use of extrapolation procedures. Several examples are considered illustrating our results as well as the use of graded meshes and the application of higher order methods. keywords Volterra integral equations; weakly s...

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...

In this paper, we present a method for solving the rst kind Abel integral equation. In thismethod, the rst kind Abel integral equation is transformed to the second kind Volterraintegral equation with a continuous kernel and a smooth deriving term expressed by weaklysingular integrals. By using Sidi's sinm - transformation and modied Navot-Simpson'sintegration rule, an algorithm for solving this...

a numerical method for solving nonlinear fredholm-volterra integral equations of general type is presented. this method is based on replacement of unknown function by truncated series of well known chebyshev expansion of functions. the quadrature formulas which we use to calculate integral terms have been imated by fast fourier transform (fft). this is a grate advantage of this method which has...