Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 565896, 12 pages
http://dx.doi.org/10.1155/2012/565896
Research Article

Error Upper Bounds for a Computational Method for Nonlinear Boundary and Initial-Value Problems

Osvaldo Guimarães and José Roberto C. Piqueira

Escola Politécnica da Universidade de São Paulo, Avenida Professor Luciano Gualberto, Travessa 3, No. 158, 05508-900 São Paulo, SP, Brazil

Received 7 December 2011; Revised 16 January 2012; Accepted 17 January 2012

Academic Editor: Jyh Horng Chou

Copyright © 2012 Osvaldo Guimarães and José Roberto C. Piqueira. 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 work develops a computational approach for boundary and initial-value problems by using operational matrices, in order to run an evolutive process in a Hilbert space. Besides, upper bounds for errors in the solutions and in their derivatives can be estimated providing accuracy measures.