Abstract and Applied Analysis
Volume 2010 (2010), Article ID 135216, 11 pages
doi:10.1155/2010/135216
Research Article

Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems

M. I. Berenguer, D. Gámez, A. I. Garralda-Guillem, and M. C. Serrano Pérez

E.U. Arquitectura Técnica, Departamento de Matemática Aplicada, Universidad de Granada, c/ Severo Ochoa, s/n, 18071 Granada, Spain

Received 9 April 2010; Accepted 17 June 2010

Academic Editor: D. Anderson

Copyright © 2010 M. I. Berenguer 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

We obtain an approximation of the solution of the nonlinear Volterra integral equation of the second kind, by means of a new method for its numerical resolution. The main tools used to establish it are the properties of a biorthogonal system in a Banach space and the Banach fixed point theorem.