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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 1/2018

22.03.2018

Computing the Matrix Mittag-Leffler Function with Applications to Fractional Calculus

verfasst von: Roberto Garrappa, Marina Popolizio

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2018

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Abstract

The computation of the Mittag-Leffler (ML) function with matrix arguments, and some applications in fractional calculus, are discussed. In general the evaluation of a scalar function in matrix arguments may require the computation of derivatives of possible high order depending on the matrix spectrum. Regarding the ML function, the numerical computation of its derivatives of arbitrary order is a completely unexplored topic; in this paper we address this issue and three different methods are tailored and investigated. The methods are combined together with an original derivatives balancing technique in order to devise an algorithm capable of providing high accuracy. The conditioning of the evaluation of matrix ML functions is also studied. The numerical experiments presented in the paper show that the proposed algorithm provides high accuracy, very often close to the machine precision.
Vorheriger Artikel MultiGrid Preconditioners for Mixed Finite Element Methods of the Vector Laplacian
Nächster Artikel The BR1 Scheme is Stable for the Compressible Navier–Stokes Equations

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Fußnoten
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Metadaten
Titel
Computing the Matrix Mittag-Leffler Function with Applications to Fractional Calculus
verfasst von
Roberto Garrappa
Marina Popolizio
Publikationsdatum
22.03.2018
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 1/2018
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-018-0699-5

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