MATHEMATICA BOHEMICA, Vol. 127, No. 2, pp. 343-352 (2002)

$N$-widths for singularly perturbed problems

Martin Stynes, R. Bruce Kellogg

M. Stynes, Mathematics Department, National University of Ireland, Cork, Ireland, e-mail:; R. B. Kellogg, P. O. Box 698, Landrum, SC 29356, USA, e-mail:

Abstract: Kolmogorov $N$-widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the $N$-widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.

Keywords: $N$-width, singularly perturbed, differential equation, boundary value problem, convection-diffusion, reaction-diffusion

Classification (MSC2000): 41A46, 34E15, 35B25, 65L10, 65N15

Full text of the article:

[Previous Article] [Next Article] [Contents of this Number]
© 2005 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition