Numerical Solution of Fractional Order Differential Equations by Extrapolation

Diethelm, Kai ; Walz, Guido

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URN: urn:nbn:de:bsz:180-madoc-17399
Document Type: Working paper
Year of publication: 1997
The title of a journal, publication series: None
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Classification: MSC: 65L06 65D30 65L05 65B05 41A55 26A33 ,
Subject headings (SWD): Ableitung gebrochener Ordnung , Integration <Mathematik> , Extrapolation , Asymptotische Entwicklung
Keywords (English): Fractional order derivative , fractional order differential equation , quadrature , extrapolation , asymptotic expansion , trapezoidal formula
Abstract: We present an extrapolation type algorithm for the numerical solution of fractional order differential equations. It is based on the new result that the sequence of approximate solutions of these equations, computed by means of a recently published algorithm by Diethelm [6], possesses an asymptotic expansion with respect to the stepsize. From this we conclude that the application of extrapolation is justified, and we obtain a very efficient differential equation solver with practically no additional numerical costs. This is also illustrated by a number of numerical examples.
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