A numerical solution of the system linear Volterra–Stieltjes integral equations second kind has been found and analyzed using so-called generalized trapezoid rule. Conditions for estimating error have also determined justified. an example obtained proposed method is given.

In this paper, we propose a new numerical method for solution of Urysohn two dimensional mixed Volterra-Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on inverse multiquadric radial basis functions (RBFs) constructed on a set of disordered data. The method is a meshless method, because it ...

A generalization of the linear fractional integral equation u(t) = u0 + ∂−αAu(t), 1 < α < 2, which is written as a Volterra matrix–valued equation when applied as a pixel–by–pixel technique, has been proposed for image denoising (restoration, smoothing,...). Since the fractional integral equation interpolates a linear parabolic equation and a hyperbolic equation, the solution enjoys intermediat...

where f, g : I × → are given functions, λ ∈ (0, 1]. The study of quadratic integral equation has received much attention over the last thirty years or so. For instance, Cahlon and Eskin [1] prove the existence of positive solutions in the space C[0, 1] and Cα[0, 1] of an integral equation of the Chandrasekhar H-equation with perturbation. Argyros [2] investigates a class of quadratic equations ...

In this paper the hybrid block-pulse function and Bernstein polynomials are introduced to approximate the solution of linear Volterra integral equations. Both second and first kind integral equations, with regular, as well as weakly singular kernels, have been considered. Numerical examples are given to demonstrate the applicability of the proposed method. The obtained results show that the hyb...

In the present paper, we solve numerically Volterra integral equations of second kind, by the well known Galerkin method. For this, we derive a simple and efficient matrix formulation using Hermite polynomials as trial functions. Numerical examples are considered to verify the effectiveness of the proposed derivations and numerical solutions are compared with the existing methods available in t...

In this paper, we study the existence of solutions of some nonlinear Volterra integral equations by using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in Banach space. We also present some examples of the integral equation to confirm the efficiency of our results.

The main purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on a spectral approach. A Legendre-collocation method is proposed to solve the Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicate that the numerical errors (in the infinity norm) will decay exponentially provid...

AbstractAn analytic technique, combination of two methods Homotopy Perturbation Method and Variational Iteration Method are applied for solve second kind of linear Volteera equations. homotopy perturbation method and variational iteration method are employed to solve Volteera integral equations. The result reveals that the homotopy perturbation method and variational iteration method are very e...