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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 985120, 8 pages
Research Article

A Zero-Dissipative Phase-Fitted Fourth Order Diagonally Implicit Runge-Kutta-Nyström Method for Solving Oscillatory Problems

1Department of Mathematics, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
2Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

Received 22 March 2014; Revised 7 May 2014; Accepted 7 May 2014; Published 25 May 2014

Academic Editor: Mohamed Abd El Aziz

Copyright © 2014 K. W. Moo 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.


A new diagonally implicit Runge-Kutta-Nyström (DIRKN) method is constructed for solving second order differential equations with oscillatory solutions. The method is originally based on existing DIRKN method derived by Senu et al. which is three-stage and fourth algebraic order. The new derived method has a variable coefficient with phase-lag of order infinity. The numerical experiments are carried out and the results show the efficiency and accuracy of the new method in comparison with the other DIRKN methods in the literature.