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Journal of Applied Mathematics
Volume 2017, Article ID 8510948, 8 pages
https://doi.org/10.1155/2017/8510948
Research Article

Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations

Department of Mathematics, School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia, Sintok, Malaysia

Correspondence should be addressed to Mohammad Alkasassbeh; moc.oohay@hebssasakfm

Received 25 August 2016; Revised 20 October 2016; Accepted 23 October 2016; Published 18 January 2017

Academic Editor: Mehmet Sezer

Copyright © 2017 Mohammad Alkasassbeh and Zurni Omar. 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

A new one-step block method with generalized three hybrid points for solving initial value problems of second-order ordinary differential equations directly is proposed. In deriving this method, a power series approximate function is interpolated at while its second and third derivatives are collocated at all points in the given interval. The proposed method is then tested on initial value problems of second-order ordinary differential equations solved by other methods previously. The numerical results confirm the superiority of the new method to the existing methods in terms of accuracy.