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.
Author: | Kai Diethelm |
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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): | Creative Commons - CC BY - Namensnennung 4.0 International |