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.