Journal of Applied Mathematics
Volume 2013 (2013), Article ID 848163, 4 pages
http://dx.doi.org/10.1155/2013/848163
Research Article

A Note on Four-Dimensional Symmetry Algebras and Fourth-Order Ordinary Differential Equations

A. Fatima,1 Muhammad Ayub,2 and F. M. Mahomed1

1Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg 2050, South Africa
2Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad 22060, Pakistan

Received 12 November 2012; Accepted 24 December 2012

Academic Editor: Mehmet Pakdemirli

Copyright © 2013 A. Fatima 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

We provide a supplementation of the results on the canonical forms for scalar fourth-order ordinary differential equations (ODEs) which admit four-dimensional Lie algebras obtained recently. Together with these new canonical forms, a complete list of scalar fourth-order ODEs that admit four-dimensional Lie algebras is available.