Three algorithms for Hadamard finite-part integrals and fractional derivatives

DOI10.1016/0377-0427(94)00113-5zbMath0858.65019OpenAlexW1994511284WikidataQ127939658 ScholiaQ127939658MaRDI QIDQ1917830

David L. Elliott

Publication date: 25 March 1997

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(94)00113-5

zbMATH Keywords

algorithmsstabilityconvergenceChebyshev polynomialsfractional derivativesnumerical examplespolynomial interpolationChebyshev series expansionHadamard finite part integral

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (6)

Finite difference methods with non-uniform meshes for nonlinear fractional differential equations ⋮ The practical Gauss type rules for Hadamard finite-part integrals using Puiseux expansions ⋮ Uniform approximations to finite Hilbert transform and its derivative. ⋮ A Chebyshev quadrature rule for one sided finite part integrals ⋮ On the Chebyshev quadrature rule of finite part integrals ⋮ Sinc approximation of Cauchy-type integrals over arcs

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• The evaluation and application of some modified moments
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• An Elementary Simultaneous Approximation Theorem
• Some Estimates of the Coefficients in the Chebyshev Series Expansion of a Function
• On the convergence of polynomials interpolating at the zeroes ofT n (x)
• The Evaluation and Estimation of the Coefficients in the Chebyshev Series Expansion of a Function

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