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Journal of Scientific Computing

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01.06.2021

A Rational Approximation Scheme for Computing Mittag-Leffler Function with Discrete Elliptic Operator as Input

verfasst von: Beiping Duan, Zhimin Zhang

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2021

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In this work, we propose a new scheme based on numerical quadrature to calculate the two-parameter Mittag-Leffler function with discrete elliptic operator \(-{\mathcal {L}}_h\) as input. Except pure mathematical interest from approximation theory, our consideration also arises from solving sub-diffusion equations numerically with time-independent diffusion coefficient. We obtain the scheme by applying Gauss-Legendre quadrature rule for the integral representation of the Mittag-Leffler function. Rigorous error analysis is carried out which shows that the scheme converges exponentially with the increase of quadrature nodes. The computational cost of the algorithm is solving K sparse linear systems with K the number of quadrature nodes. It is worth to point out that the scheme is completely parallel which can save much time if the dimension of \({\mathcal {L}}_h\) is very large. Some numerical tests are provided to verify the efficiency and robustness of our scheme.

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Titel: A Rational Approximation Scheme for Computing Mittag-Leffler Function with Discrete Elliptic Operator as Input
verfasst von: Beiping Duan
Zhimin Zhang
Publikationsdatum: 01.06.2021
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2021
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-021-01495-y

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