International Journal of Mathematics and Mathematical Sciences 
Volume 2008 (2008), Article ID 364021, 10 pages
doi:10.1155/2008/364021
Research Article

An Efficient Zero-Stable Numerical Method for Fourth-Order Differential Equations

S. J. Kayode

 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

Recommended by Michael Evans

Abstract

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 p=6. The main predictor for the method is also consistent, symmetric, zero-stable, and of optimal order p=6.