International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 364021, 10 pages
An Efficient Zero-Stable Numerical Method for
Fourth-Order Differential Equations
Department of Mathematical Sciences, School of Sciences, Federal University of Technology, PMB 704, Akure, Ondo State, Nigeria
Received 9 July 2007; Revised 26 February 2008; Accepted 9 April 2008
Academic Editor: Michael Evans
Copyright © 2008 S. J. Kayode. 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.
The purpose of this paper is to produce an efficient zero-stable numerical
method with the same order of accuracy as that of the main starting values (predictors) for direct solution of fourth-order differential equations without reducing it to a system of first-order equations. The method of collocation of the differential system arising from the approximate solution to the problem is adopted using the power series as a basis function. The method is consistent, symmetric, and of optimal order .
The main predictor for the method is also consistent, symmetric, zero-stable, and of optimal order .