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International Journal of Engineering Mathematics
Volume 2015, Article ID 650425, 14 pages
http://dx.doi.org/10.1155/2015/650425
Research Article

Block Backward Differentiation Formulas for Fractional Differential Equations

1Department of Mathematics and Computer Science, Sule Lamido University, Kafin Hausa, PMB 048, Kafin Hausa, Nigeria
2Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, USA

Received 20 May 2015; Accepted 14 July 2015

Academic Editor: Yurong Liu

Copyright © 2015 T. A. Biala and S. N. Jator. 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 concerns the numerical approximation of Fractional Initial Value Problems (FIVPs). This is achieved by constructing -step continuous BDFs. These continuous schemes are developed via the interpolation and collocation approach and are used to obtain the discrete -step BDF and () additional methods which are applied as numerical integrators in a block-by-block mode for the integration of FIVP. The properties of the methods are established and regions of absolute stability of the methods are plotted in the complex plane. Numerical tests including large systems arising form the semidiscretization of one-dimensional fractional Burger’s equation show that the methods are highly accurate and efficient.