Research Article A 4-Point Block Method for Solving Higher Order Ordinary Differential Equations Directly Nazreen Waeleh 1 and Zanariah Abdul Majid 2,3 1 Faculty of Electronic & Computer Engineering, Universiti Teknikal Malaysia Melaka (UTeM), 76100 Melaka, Malaysia 2 Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia 3 Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia Correspondence should be addressed to Nazreen Waeleh; nazreen@utem.edu.my Received 18 April 2016; Revised 23 June 2016; Accepted 30 June 2016 Academic Editor: Harvinder S. Sidhu Copyright © 2016 N. Waeleh and Z. Abdul Majid. Tis 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. An alternative block method for solving ffh-order initial value problems (IVPs) is proposed with an adaptive strategy of implementing variable step size. Te derived method is designed to compute four solutions simultaneously without reducing the problem to a system of frst-order IVPs. To validate the proposed method, the consistency and zero stability are also discussed. Te 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 ffh-order IVPs. 1. Introduction Many natural processes or real-world problems can be trans- lated into the language of mathematics [1–4]. Te mathe- matical formulation of physical phenomena in science and engineering ofen leads to a diferential equation, which can be categorized as an ordinary diferential equation (ODE) and a partial diferential equation (PDE). Tis formulation will explain the behavior of the phenomenon in detail. Te search for solutions of real-world problems requires solving ODEs and thus has been an important aspect of mathematical study. For many interesting applications, an exact solution may be unattainable, or it may not give the answer in a convenient form. Te reliability of numerical approximation techniques in solving such problems has been proven by many researchers as the role of numerical methods in engineering problems solving has increased dramatically in recent years. Tus a numerical approach has been chosen as an alternative tool for approximating the solutions consistent with the advancement in technology. Commonly, the formulation of real-world problems will take the form of a higher order diferential equation asso- ciated with its initial or boundary conditions [4]. In the literature, a mathematical model in the form of a ffh-order diferential equation, known as Korteweg-de Vries (KdV) equation, has been used to describe several wave phenomena depending on the values of its parameters [2, 3, 5, 6]. Te KdV equation is a PDE and researchers have tackled the problem analytically and numerically. It is also noted that in certain cases by using diferent approaches the KdV might be transformed into a higher order ODE [7]. To date, there are a number of studies that have proposed solving ffh-order ODE directly [8, 9]. Hence, the purpose of the present paper is to solve directly the ffh-order IVPs with the implementation of a variable step size strategy. Te ffh-order IVP with its initial conditions is defned as  v =(,,  ,  ,  , iv ), ()= 0 ,  ()= 1 ,  ()= 2 ,  ()= 3 , iv ()= 4 ,∈[,]. (1) Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2016, Article ID 9823147, 8 pages http://dx.doi.org/10.1155/2016/9823147