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An Improvement of a Nonclassical Numerical Method for the Computation of Fractional Derivatives

  • Standard methods for the numerical calculation of fractional derivatives can be slow and memory consuming due to the nonlocality of the differential operators. Yuan and Agrawal (2002, “A Numerical Scheme for Dynamic Systems Containing Fractional Derivatives,” ASME J. Vibr. Acoust., 124, pp. 321–324) have proposed a more efficient approach for operators whose order is between 0 and 1 that differs substantially from the traditional concepts. It seems, however, that the accuracy of the results can be poor. We modify the approach, adapting it better to the properties of the problem, and show that this leads to a significantly improved quality. Our idea also works for operators of order greater than 1.

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Metadaten
Author:Kai Diethelm
URN:urn:nbn:de:bvb:863-opus-20688
Persistent identifier:https://asmedigitalcollection.asme.org/vibrationacoustics/article-abstract/131/1/014502/471073/An-Improvement-of-a-Nonclassical-Numerical-Method
DOI:https://doi.org/10.1115/1.2981167
Parent Title (English):Journal of Vibration and Acoustics
Document Type:Article
Language:English
Year of publication:2009
Publishing Institution:Hochschule für Angewandte Wissenschaften Würzburg-Schweinfurt
Release Date:2022/07/25
Tag:differential equations; fractional derivative; numerical analysis
Volume:131
Issue:1
Article Number:014502
Pages/Size:4
Comments:
Accepted Version des Artikels.
© ASME
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 518 Numerische Analysis
Regensburger Klassifikation:Mathematik
Open access colour:Grün (Zweitveröffentlichung)
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International
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