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A survey of numerical techniques for solving singularly perturbed ordinary differential equations. (English) Zbl 1026.65059
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.

65L10Boundary value problems for ODE (numerical methods)
65L05Initial value problems for ODE (numerical methods)
65-02Research monographs (numerical analysis)
34B05Linear boundary value problems for ODE
34A30Linear ODE and systems, general
34E15Asymptotic singular perturbations, general theory (ODE)