Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 862538, 18 pages
doi:10.1155/2010/862538
Research Article

On the Stability of Numerical Methods for Nonlinear Volterra Integral Equations

E. Messina,1 Y. Muroya,2 E. Russo,1 and A. Vecchio3

1Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, Via Cintia, 80126 Napoli, Italy
2Department of Mathematics, Waseda University, 3-4-1 Ohkubo Shinjuku-ku, Tokyo, 169-8555, Japan
3Istituto per le Applicazioni del Calcolo “M.Picone”, Sede di Napoli, CNR, Via P. Castellino, 80131 Napoli, Italy

Received 3 March 2010; Accepted 12 May 2010

Academic Editor: Manuel De la Sen

Copyright © 2010 E. Messina et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Here we investigate the behavior of the analytical and numerical solution of a nonlinear second kind Volterra integral equation where the linear part of the kernel has a constant sign and we provide conditions for the boundedness or decay of solutions and approximate solutions obtained by Volterra Runge-Kutta and Direct Quadrature methods.