Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 193691, 12 pages
http://dx.doi.org/10.1155/2011/193691
Research Article

A Quantitative Comparison of Numerical Method for Solving Stiff Ordinary Differential Equations

S. A. M. Yatim,1 Z. B. Ibrahim,1 K. I. Othman,2 and M. B. Suleiman1

1Department of Mathematics, Faculty of Science, Universiti Putra Malaysia (UPM), Selangor, 43400 Serdang, Malaysia
2Department of Mathematics, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Selangor, 40450 Shah Alam, Malaysia

Received 17 April 2011; Accepted 28 June 2011

Academic Editor: Claude Lamarque

Copyright © 2011 S. A. M. Yatim 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

We derive a variable step of the implicit block methods based on the backward differentiation formulae (BDF) for solving stiff initial value problems (IVPs). A simplified strategy in controlling the step size is proposed with the aim of optimizing the performance in terms of precision and computation time. The numerical results obtained support the enhancement of the method proposed as compared to MATLAB's suite of ordinary differential equations (ODEs) solvers, namely, ode15s and ode23s.