A brief survey on numerical methods for solving singularly perturbed problems

• Published in: Applied mathematics and computation Vol. 217; no. 8; pp. 3641 - 3716
• Main Authors: Kadalbajoo, Mohan K., Gupta, Vikas
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 15.12.2010; Elsevier
• Subjects: Boundary layers; Computation; Exact sciences and technology; Layer adapted meshes; Mathematical analysis; Mathematical models; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Sciences and techniques of general use; Singular perturbation; Uniform convergence; Uniform convergence; Layer adapted meshes; Singular perturbation; Boundary layers; Perturbation method; Numerical analysis; Applied mathematics; Problem solving; Numerical method; Stochastic method; Boundary layer
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2010.09.059

In the present paper, a brief survey on computational techniques for the different classes of singularly perturbed problems is given. This survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000–2009. However some older important relevant papers are also included in this survey. We also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper, see [Appl. Math. Comput. 30 (1989) 223–259, 130 (2002) 457–510, 134 (2003) 371–429] for details. Thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems.