A Recent Development of Computer Methods for Solving Singularly Perturbed Boundary Value Problems

Abstract

This paper contains a surprisingly large amount of material and indeed can serve as an introduction to some of ideas and methods of singular perturbation theory. The work done in this area during the periods 1984–2000 and 2000–2005 has already been surveyed in 2002 and 2007 but our main objective is to produce a collection of important research articles of physical significance. In this paper, the crux of research articles published by numerous researchers during 2006–2010 in referred journals has been presented, and this leads to conclusions and recommendations about what methods to use on singular perturbation problems.

A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions

“…In 2010, Kadalbajoo and Gupta in their study Kadalbajoo and Gupta ( 2010 ) made a great survey on the numerical methods for singularly perturbed problems. In 2011, Parul studied the traditional methods to solve this kind of problems and gave important examples occuring in engineering and science (Kumar 2011 , 2011 ). In 2012, Roos made a survey, particularly of singularly perturbed convection–reaction–diffusion problems covering the years 2008–2012 (Roos 2012 ).…”