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American Journal of Applied Mathematics and Statistics. 2014, 2(3), 129-142
DOI: 10.12691/AJAMS-2-3-7
Review Article

Various Numerical Methods for Singularly Perturbed Boundary Value Problems

Hradyesh Kumar Mishra1, and Sonali saini1

1Department of Mathematics, Jaypee University of Engineering &Technology, Madhya Pradesh, India

Pub. Date: May 09, 2014
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Cite this paper

Hradyesh Kumar Mishra and Sonali saini. Various Numerical Methods for Singularly Perturbed Boundary Value Problems. American Journal of Applied Mathematics and Statistics. 2014; 2(3):129-142. doi: 10.12691/AJAMS-2-3-7

Abstract

The numerical treatment of singular perturbation problems is currently a field in which active research is going on these days. Singular perturbation problems in which the term containing the highest order derivative is multiplied by a small parameter ε, occur in a number of areas of applied mathematics, science and engineering among them fluid mechanics (boundary layer problems) elasticity (edge effort in shells) and quantum mechanics. In this paper, we consider few numerical methods for singularly perturbed boundary value problems developed by numerous researchers between 2006 to 2013. A Summary of the result of some recent methods is presented and this leads to conclusion and recommendations regarding methods to use on singular perturbation problem.

Keywords

singular perturbation, ordinary differential equation, boundary layer, two-point boundary value problem, delay differential equations, integral equations

Copyright

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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