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Zbl 1026.65059
Kadalbajoo, Mohan K.; Patidar, Kailash C.
A survey of numerical techniques for solving singularly perturbed ordinary differential equations. (English)
[J] Appl. Math. Comput. 130, No.2-3, 457-510 (2002). ISSN 0096-3003

Summary: This survey paper contains a surprisingly large amount of material and indeed can serve as an introduction to some of the ideas and methods of singular perturbation theory. Starting from Prandtl's work a large amount of work has been done in the area of singular perturbations. This paper limits its coverage to some standard singular perturbation models considered by various workers and the numerical methods developed by numerous researchers after 1984-2000. The work done in this area during the period 1905-1984 has already been surveyed by the first author of this paper [Appl. Math. Comput. 30, No. 3, 223-259 (1989; Zbl 0678.65059)] for details. Due to the space constraints we have covered only singularly perturbed one-dimensional problems.

MSC 2000:: *65L10 Boundary value problems for ODE (numerical methods)
65L05 Initial value problems for ODE (numerical methods)
65-02 Research monographs (numerical analysis)
34B05 Linear boundary value problems of ODE
34A30 Linear ODE and systems
34E15 Asymptotic singular perturbations, general theory (ODE)

Keywords: research survey; singular perturbations; initial and boundary value problems

Citations: Zbl 0678.65059

Cited in: Zbl 1208.65105 Zbl 1127.65053

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