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A recent survey on computational techniques for solving singularly perturbed boundary value problems. (English) Zbl 1127.65053
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 [M. K. Kadalbajoo and Y. N. Reddy, Appl. Math. Comput. 30, No. 3, 223–259 (1989; Zbl 0678.65059); M. K. Kadalbajoo and 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:
65L10Boundary value problems for ODE (numerical methods)
34B05Linear boundary value problems for ODE
34E15Asymptotic singular perturbations, general theory (ODE)
65-02Research monographs (numerical analysis)
65L20Stability and convergence of numerical methods for ODE