ON THE COMPARISON OF ERROR-BOUNDS FOR FINITE-DIFFERENCE SCHEMES

In 1968 Sendov and Korovkin independently introduced the T-Modulus as a new measure for the smoothness of functions which already has found various applications in approximation theory and numerical analysis. H ere it is employed to derive sharp error bounds for the approximate so lution of linear two-point boundary value problems for ordinary differ ential equations. These indeed improve corresponding estimates in term s of ordinary (L(infinity) -) moduli of continuity. Finally, the effec t is also discussed in the light of a quantitative resonance theorem.