A general approach to counterexamples in numerical analysis
A general theorem is proved concerning the existence of functions which are smooth according to one generalized modulus of continuity and not smooth according to another. This theorem is then applied to several specific cases, including estimates for the trapezoid rule and Simpson's rule for quadrature. Examples concerning the rate of convergence of a method of lines for the heat equation are also presented.
scientific article; zbMATH DE number 3905165
scientific article