A recent survey on computational techniques for solving singularly perturbed boundary value problems

Authors:
Manoj Kumar;Pitam Singh;Hradyesh Kumar Mishra
Affiliations:
Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad-, (U.P), India;Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad-, (U.P), India;Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad-, (U.P), India
Venue:
International Journal of Computer Mathematics
Year:
2007

Citing 24
Cited 3

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Abstract

This survey 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. In continuation of a survey performed earlier, this paper limits its coverage to some standard numerical methods developed by numerous researchers between 2000 and 2005. A summary of the results of some recent methods is presented and this leads to conclusions and recommendations regarding methods to use on singular perturbation problems. Because of space constraints, we considered one-dimensional singularly perturbed boundary value problems only.