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Discrete Dynamics in Nature and Society
Volume 2018 (2018), Article ID 2393015, 10 pages
https://doi.org/10.1155/2018/2393015
Research Article

Efficient Two-Derivative Runge-Kutta-Nyström Methods for Solving General Second-Order Ordinary Differential Equations

1Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2Department of Mathematics, Faculty of Science, Misrata University, Misrata, Libya
3Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Correspondence should be addressed to N. Senu; ym.ude.mpu@kazaron

Received 17 September 2017; Revised 2 January 2018; Accepted 5 February 2018; Published 20 March 2018

Academic Editor: Ciprian G. Gal

Copyright © 2018 T. S. Mohamed 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

This paper proposes and investigates a special class of explicit Runge-Kutta-Nyström (RKN) methods for problems in the form including third derivatives and denoted as STDRKN. The methods involve one evaluation of second derivative and many evaluations of third derivative per step. In this study, methods with two and three stages of orders four and five, respectively, are presented. The stability property of the methods is discussed. Numerical experiments have clearly shown the accuracy and the efficiency of the new methods.