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In this paper, we discuss the application of an iterative collocation method based on the use of Lagrange polynomials for the numerical solution of a class of nonlinear third-kind Volterra integral equations. The approximate solution is given by explicit formulas. The error analysis of the proposed numerical method is studied theoretically. Some numerical examples are given to confirm our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the numerical solution of a two‐dimensional partial Volterra integro‐differential equation (2D‐PVIDE) is provided by extending the Taylor collocation scheme of one‐dimensional Volterra integral equations. The method is based on the use of Taylor polynomials in two‐dimensional, while the approximate solution is given by using explicit schemes. The method is proved to be high‐order convergent with respect to the maximum norm. Some numerical examples are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an iterative collocation method is presented for a class of nonlinear Volterra integro-differential equations. This iterative collocation method is made by using a suitable continuous spline polynomials. It is shown that this method is convergent. The results are compared with the results obtained by other well-known numerical methods to prove the effectiveness of the presented algorithm. [ABSTRACT FROM AUTHOR]

The main purpose of this work is to provide a new direct numerical method for high-order linear Volterra integro-differential equations (VIDEs). An algorithm based on the use of Taylor polynomials is developed for the numerical solution of high-order linear VIDEs. It is shown that this algorithm is convergent. Numerical results are presented and comparisons are made with well-known numerical methods to prove the effectiveness of the presented algorithm. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical solution of delay integro-differential equations. The main purpose of this work is to provide a new numerical approach based on the use of continuous collocation Taylor polynomials for the numerical solution of delay integro-differential equations. It is shown that this method is convergent. Numerical illustrations confirm our theoretical analysis. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A numerical method based on the use of Taylor polynomials is proposed to construct a collocation solution $u\in S_{m-1}^{(-1)}(\Pi _{N})$ for approximating the solution of delay integral equations. It is shown that this method is convergent. Some numerical examples are given to show the validity of the presented method. [ABSTRACT FROM AUTHOR]

The main purpose of this work is to provide a numerical approach for two-dimensional Volterra integral equations (2D-VIEs). An algorithm based on the use of Taylor polynomials is developed to construct a collocation solution v ∈ S p − 1 , p − 1 (− 1) (Π N , M) for approximating the solution of 2D-VIEs. It is shown that this algorithm is convergent. Some numerical examples are included to demonstrate the accuracy of the presented method. [ABSTRACT FROM AUTHOR]