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International Journal of Mathematics and Mathematical Sciences
Volume 2016, Article ID 9823147, 8 pages
http://dx.doi.org/10.1155/2016/9823147
Research Article

A 4-Point Block Method for Solving Higher Order Ordinary Differential Equations Directly

1Faculty of Electronic & Computer Engineering, Universiti Teknikal Malaysia Melaka (UTeM), 76100 Melaka, Malaysia
2Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
3Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 18 April 2016; Revised 23 June 2016; Accepted 30 June 2016

Academic Editor: Harvinder S. Sidhu

Copyright © 2016 Nazreen Waeleh and Zanariah Abdul Majid. 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 alternative block method for solving fifth-order initial value problems (IVPs) is proposed with an adaptive strategy of implementing variable step size. The derived method is designed to compute four solutions simultaneously without reducing the problem to a system of first-order IVPs. To validate the proposed method, the consistency and zero stability are also discussed. The improved performance of the developed method is demonstrated by comparing it with the existing methods and the results showed that the 4-point block method is suitable for solving fifth-order IVPs.