Sequences of errors with boundary layer in spaces of univariate functions with fractional Riemann-Liouville derivatives (Q1876440)
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scientific article; zbMATH DE number 2097381
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sequences of errors with boundary layer in spaces of univariate functions with fractional Riemann-Liouville derivatives |
scientific article; zbMATH DE number 2097381 |
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Sequences of errors with boundary layer in spaces of univariate functions with fractional Riemann-Liouville derivatives (English)
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7 September 2004
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The author studies the asymptotics of errors for complicated quadrature formulas and formulas with boundary layer on functions with fractional Riemann-Liouville derivatives summable to some power. It is shown that the formulas under consideration are asymptotically best with respect to the rate of convergence among formulas with arbitrary nodes and weights. The results obtained are illustrated by the examples of trapezoidal and rectangle rules. This is an English translation of the author's article [Mat. Tr. 5, No. 2, 178--202 (2002; Zbl 1013.41017)].
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quadrature formula
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fractional derivative
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error
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0.7722333073616028
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0.767798125743866
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