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Efficient Implementation of Rational Approximations to Fractional Differential Operators

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Abstract

This paper deals with some numerical issues about the rational approximation to fractional differential operators provided by the Padé approximants. In particular, the attention is focused on the fractional Laplacian and on the Caputo’s derivative which, in this context, occur into the definition of anomalous diffusion problems and of time fractional differential equations (FDEs), respectively. The paper provides the algorithms for an efficient implementation of the IMEX schemes for semi-discrete anomalous diffusion problems and of the short-memory-FBDF methods for Caputo’s FDEs.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, via F. Buonarroti, 1/C, 56127, Pisa, Italy

    Lidia Aceto

  2. Dipartimento di Matematica e Geoscienze, Università di Trieste, via Valerio 12/1, 34127, Trieste, Italy

    Paolo Novati

Authors
  1. Lidia Aceto
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  2. Paolo Novati
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Correspondence to Lidia Aceto.

Additional information

This work was partially supported by GNCS-INdAM, University of Pisa (Grant PRA_2017_05) and FRA-University of Trieste.

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Aceto, L., Novati, P. Efficient Implementation of Rational Approximations to Fractional Differential Operators. J Sci Comput 76, 651–671 (2018). https://doi.org/10.1007/s10915-017-0633-2

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  • DOI: https://doi.org/10.1007/s10915-017-0633-2

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