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Zbl 1127.65053
Kumar, Manoj; Singh, Pitam; Kumar Mishra, Hradyesh
A recent survey on computational techniques for solving singularly perturbed boundary value problems. (English)
[J] Int. J. Comput. Math. 84, No. 10, 1439-1463 (2007). ISSN 0020-7160; ISSN 1029-0265/e

Summary: This survey paper contains a surprisingly large amount of material and indeed can serve as an introduction to some of ideas and methods of the singular perturbation theory. In continuation of a survey performed earlier [{\it M. K. Kadalbajoo} and {\it Y. N. Reddy}, Appl. Math. Comput. 30, No.~3, 223--259 (1989; Zbl 0678.65059); {\it M. K. Kadalbajoo} and {\it K. C. Patidar}, ibid. 130, No.~2--3, 457--510 (2002; Zbl 1026.65059)], 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.

MSC 2000:: *65L10 Boundary value problems for ODE (numerical methods)
34B05 Linear boundary value problems of ODE
34E15 Asymptotic singular perturbations, general theory (ODE)
65-02 Research monographs (numerical analysis)
65L20 Stability of numerical methods for ODE

Keywords: singular perturbations; reaction-diffusion; uniform convergence; boundary value problems; survey paper

Citations: Zbl 0678.65059; Zbl 1026.65059

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Zentralblatt MATH Berlin [Germany]