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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 182536, 15 pages
http://dx.doi.org/10.1155/2012/182536
Research Article

New Stable Closed Newton-Cotes Trigonometrically Fitted Formulae for Long-Time Integration

1Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, 221 00 Tripolis, Greece

Received 2 January 2012; Accepted 16 February 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 T. E. Simos. 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

The closed Newton-Cotes differential methods of high algebraic order for small number of function evaluations are unstable. In this work, we propose a new closed Newton-Cotes trigonometrically fitted differential method of high algebraic order which gives much more efficient results than the well-know ones.