Table of Contents
ISRN Applied Mathematics
Volume 2013 (2013), Article ID 567451, 10 pages
http://dx.doi.org/10.1155/2013/567451
Research Article

An Accurate Block Solver for Stiff Initial Value Problems

1Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 19 June 2013; Accepted 20 July 2013

Academic Editors: S. Blanes and L. You

Copyright © 2013 H. Musa 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

New implicit block formulae that compute solution of stiff initial value problems at two points simultaneously are derived and implemented in a variable step size mode. The strategy for changing the step size for optimum performance involves halving, increasing by a multiple of 1.7, or maintaining the current step size. The stability analysis of the methods indicates their suitability for solving stiff problems. Numerical results are given and compared with some existing backward differentiation formula algorithms. The results indicate an improvement in terms of accuracy.