International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 767328, 8 pages
http://dx.doi.org/10.1155/2012/767328
Research Article

Diagonally Implicit Block Backward Differentiation Formulas for Solving Ordinary Differential Equations

I. S. M. Zawawi,1 Z. B. Ibrahim,2 F. Ismail,2 and Z. A. Majid2

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

Received 3 June 2012; Revised 9 October 2012; Accepted 14 October 2012

Academic Editor: Attila Gilányi

Copyright © 2012 I. S. M. Zawawi 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

This paper focuses on the derivation of diagonally implicit two-point block backward differentiation formulas (DI2BBDF) for solving first-order initial value problem (IVP) with two fixed points. The method approximates the solution at two points simultaneously. The implementation and the stability of the proposed method are also discussed. A performance of the DI2BBDF is compared with the existing methods.