Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 591341, 15 pages
doi:10.1155/2010/591341
Research Article

A Zero-Dissipative Runge-Kutta-Nyström Method with Minimal Phase-Lag

Norazak Senu,1 Mohamed Suleiman,1 Fudziah Ismail,1 and Mohamed Othman2

1Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, UPM Serdang, 43400 Selangor, Malaysia
2Department of Communication Technology and Network, Faculty of Computer Science and Information Technology, Universiti Putra Malaysia, UPM Serdang, 43400 Selangor, Malaysia

Received 28 October 2009; Revised 29 January 2010; Accepted 6 May 2010

Academic Editor: Yuri Vladimirovich Mikhlin

Copyright © 2010 Norazak Senu 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

An explicit Runge-Kutta-Nyström method is developed for solving second-order differential equations of the form q′′=f(t,q) where the solutions are oscillatory. The method has zero-dissipation with minimal phase-lag at a cost of three-function evaluations per step of integration. Numerical comparisons with RKN3HS, RKN3V, RKN4G, and RKN4C methods show the preciseness and effectiveness of the method developed.