Abstract and Applied Analysis
Volume 2012 (2012), Article ID 239695, 9 pages
http://dx.doi.org/10.1155/2012/239695
Research Article

Some New Estimates for the Error of Simpson Integration Rule

Mohammad Masjed-Jamei,1 Marwan A. Kutbi,2 and Nawab Hussain2

1Department of Mathematics, K. N. Toosi University of Technology, Tehran 19697, Iran
2Department of Mathematics, King AbdulAziz University, Jeddah 21589, Saudi Arabia

Received 9 September 2012; Accepted 10 October 2012

Academic Editor: Mohammad Mursaleen

Copyright © 2012 Mohammad Masjed-Jamei 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 some new estimates for the error of Simpson integration rule, which develop available results in the literature. Indeed, we introduce three main estimates for the residue of Simpson integration rule in and spaces where the compactness of the interval plays a crucial role.