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

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.

Keywords:

• Singular perturbations
• Computational methods
• Reaction-diffusion
• Uniform convergence
• Boundary value problems

Acknowledgements

We wish to express our sincere thanks to Professor Taketomo Mitsui, Graduate School of Information Science, Nagoya University, Japan and Professor R.C. Mittal, Department of Mathematics, Indian Institute of Technology, Roorkee, India, for their comments and suggestions.

Additional information

Notes on contributors

Pitam Singh

Email: [email protected]

Hradyesh Kumar Mishra

Email: [email protected]