Diagonally Implicit Super Class of Block Backward Differentiation Formula with OffÃ¢ÂÂStep Points for Solving Stiff Initial Value Problems
Babangida B* and Musa H
Department of Mathematics and Computer Sciences, Umaru Musa Yar'adua University, Katsina, Nigeria
- *Corresponding Author:
- Babangida B
Department of Mathematics and Computer Sciences
Faculty of Natural and Applied Sciences
Umaru Musa Yar'adua University
E-mail: [email protected]
Received Date: September 13, 2016; Accepted Date: September 27, 2016; Published Date: October 03, 2016
Citation: Babangida B, Musa H (2016) Diagonally Implicit Super Class of Block Backward Differentiation Formula with Off-Step Points for Solving Stiff Initial Value Problems. J Appl Computat Math 5: 324. doi: 10.4172/2168-9679.1000324
Copyright: © 2016 Babangida B, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
A new formula called 2-point diagonally implicit super class of BBDF with two off-step points (2ODISBBDF) for solving stiff IVPs is formulated. The method approximates two solutions with two off-step points simultaneously at each iteration. By varying a parameter ρ ∈ (–1,1) in the formula, different sets of formulae can be generated. A specific choice of ρ =3/4 is made and it was shown that the method is both zero and A-stable. A comparison between the new method and the existing 2-point block backward differentiation formula with off-step points (2OBBDF) is made. The results show that the new method outperformed existing 2OBBDF method in terms of accuracy.