Journal of Applied Mathematics
Volume 2012 (2012), Article ID 263570, 15 pages
http://dx.doi.org/10.1155/2012/263570
Research Article

Symmetries of th-Order Approximate Stochastic Ordinary Differential Equations

E. Fredericks1 and F. M. Mahomed2

1Department of Mathematics and Applied Mathematics, University of Cape Town, Room 310.1, Rondebosch 7700, South Africa
2Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg 2050, South Africa

Received 26 September 2012; Accepted 9 November 2012

Academic Editor: Asghar Qadir

Copyright © 2012 E. Fredericks and F. M. Mahomed. 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

Symmetries of th-order approximate stochastic ordinary differential equations (SODEs) are studied. The determining equations of these SODEs are derived in an Itô calculus context. These determining equations are not stochastic in nature. SODEs are normally used to model nature (e.g., earthquakes) or for testing the safety and reliability of models in construction engineering when looking at the impact of random perturbations.