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: