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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 989381, 11 pages
Research Article

A Numerical Algorithm for Solving Stiff Ordinary Differential Equations

1School of Distance Education, Universiti Sains Malaysia, 11800 Penang, Malaysia
2Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor, 43400 Serdang, Malaysia
3Department of Mathematics, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Selangor, 40450 Shah Alam, Malaysia

Received 6 August 2012; Revised 24 October 2012; Accepted 7 November 2012

Academic Editor: J. Rodellar

Copyright © 2013 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.


An advanced method using block backward differentiation formula (BBDF) is introduced with efficient strategy in choosing the step size and order of the method. Variable step and variable order block backward differentiation formula (VSVO-BBDF) approach is applied throughout the numerical computation. The stability regions of the VSVO-BBDF method are investigated and presented in distinct graphs. The improved performances in terms of accuracy and computation time are presented in the numerical results with different sets of test problems. Comparisons are made between the proposed method and MATLAB’s suite of ordinary differential equations (ODEs) solvers, namely, ode15s and ode23s.