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Mathematical Problems in Engineering
Volume 2011, Article ID 810324, 18 pages
http://dx.doi.org/10.1155/2011/810324
Research Article

Solution of Higher-Order ODEs Using Backward Difference Method

Department of Mathematics, Faculty of Science, UPM, Selangor Darul Ehsan, 43400 Serdang, Malaysia

Received 9 November 2010; Revised 25 March 2011; Accepted 13 May 2011

Academic Editor: Francesco Pellicano

Copyright © 2011 Mohamed Bin Suleiman 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

The current numerical technique for solving a system of higher-order ordinary differential equations (ODEs) is to reduce it to a system of first-order equations then solving it using first-order ODE methods. Here, we propose a method to solve higher-order ODEs directly. The formulae will be derived in terms of backward difference in a constant stepsize formulation. The method developed will be validated by solving some higher-order ODEs directly with constant stepsize. To simplify the evaluations of the integration coefficients, we find the relationship between various orders. The result presented confirmed our hypothesis.