In the present paper we consider the regularizing properties of linear multistep methods for the stable solution of perturbed Volterra integral equations of the first kind with smooth kernels. Numerical results are also given.

‎In this paper‎, ‎a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{beta}(t-s)^{-alpha}G(y(s))$ based on the Tau method‎. ‎In this method‎, ‎a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution‎. ‎Error analysis of this method is also ...

In this paper, we establish the existence and uniqueness results to Cauchy problem posed for a fuzzy fractional Volterra-Stieltjes integrodifferential equation. The method of successive approximations is used prove existence, whereas contraction theory applied solution problem.

This paper presents a numerical method for solving the Volterra integral equation with a convolution kernel. The integral equation was first converted to an algebraic equation using the Laplace transform, after which its numerical inversion was determined by power series. The Padé approximants were effectively used to improve the convergence rate and accuracy of the computed series. The method ...

‎in this paper‎, ‎we construct a new iterative method for solving nonlinear volterra integral equation of second kind‎, ‎by approximating the legendre polynomial basis‎. ‎error analysis is worked using banach fixed point theorem‎. ‎we compute the approximate solution without using numerical method‎. ‎finally‎, ‎some examples are given to compare the results with some of the existing methods‎.

In this study, we use Whittaker cardinal expansion and collocation method to approximate the solution of Volterra integral equation of the second kind numerically which is arisen in many mathematical, industrial and medical problems. Then convergence of this method will be discussed in L space for every positive . At the end of the paper, some numerical examples are presented to guarantee the a...