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Mathematical Problems in Engineering
Volume 2014, Article ID 565137, 10 pages
http://dx.doi.org/10.1155/2014/565137
Research Article

Solving Nonstiff Higher Order Odes Using Variable Order Step Size Backward Difference Directly

1Institute for Mathematical Research, UPM, Selangor Darul Ehsan, 43400 Serdang, Malaysia
2Department of Mathematics, Faculty of Science, UPM, Selangor Darul Ehsan, 43400 Serdang, Malaysia

Received 11 March 2014; Revised 3 July 2014; Accepted 22 July 2014; Published 19 August 2014

Academic Editor: Alessandro Palmeri

Copyright © 2014 Ahmad Fadly Nurullah Rasedee 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 techniques for solving a system of higher order ordinary differential equations (ODEs) directly calculate the integration coefficients at every step. Here, we propose a method to solve higher order ODEs directly by calculating the integration coefficients only once at the beginning of the integration and if required once more at the end. The formulae will be derived in terms of backward difference in a constant step size formulation. The method developed will be validated by solving some higher order ODEs directly using variable order step size. To simplify the evaluations of the integration coefficients, we find the relationship between various orders. The results presented confirmed our hypothesis.