Summary
In 1968 Sendov and Korovkin independently introduced the τ-modulus as a new measure for the smoothness of functions which already has found various applications in approximation theory and numerical analysis. Here it is employed to derive sharp error bounds for the approximate solution of linear two-point boundary value problems for ordinary differential equations. These indeed improve corresponding estimates in terms of ordinary (L ∞-) moduli of continuity. Finally, the effect is also discussed in the light of a quantitative resonance theorem.
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Büttgenbach, B., Esser, H. & Nessel, R.J. On the comparison of error bounds for finite difference schemes. Numer. Math. 64, 477–486 (1993). https://doi.org/10.1007/BF01388700
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DOI: https://doi.org/10.1007/BF01388700