Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 925276, 15 pages
doi:10.1155/2009/925276
Research Article

Computationally Efficient Technique for Solving ODE Systems Exhibiting Initial and Boundary Layers

N. Parumasur, P. Singh, and V. Singh

School of Mathematical Sciences, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa

Received 29 May 2009; Accepted 13 October 2009

Academic Editor: Irena Trendafilova

Copyright © 2009 N. Parumasur 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

A computational technique based on asymptotic analysis for solving singularly perturbed ODE systems involving a small parameter ϵ is considered. The focus is on second-order systems, but the procedure is also applicable for first-order systems. Both initial value and boundary value problems will be solved. The application of the method is considered over the entire time domain for a wide range of ϵ and the resulting approximation is compared with the direct numerical solution. The convection-diffusion problem from fluid mechanics and the telegraph equation from electrical engineering are considered.