Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 470149, 9 pages
doi:10.1155/2010/470149
Research Article

Biorthogonal Systems Approximating the Solution of the Nonlinear Volterra Integro-Differential Equation

M. I. Berenguer, A. I. Garralda-Guillem, and M. Ruiz Galán

Departamento de Matemática Aplicada, Escuela Universitaria de Arquitectura Técnica, Universidad de Granada, 18071 Granada, Spain

Received 22 March 2010; Accepted 14 June 2010

Academic Editor: Juan J. Nieto

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

This paper deals with obtaining a numerical method in order to approximate the solution of the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach, a sequence of functions which approximate the solution of this type of equation, due to some properties of certain biorthogonal systems for the Banach spaces C[0,1] and C[0,1]2.