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A New Diffusive Representation for Fractional Derivatives, Part II: Convergence Analysis of the Numerical Scheme

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  • Kai Diethelm

    (Faculty of Applied Natural Sciences and Humanities, University of Applied Sciences Würzburg-Schweinfurt, Ignaz-Schön-Str. 11, 97421 Schweinfurt, Germany)

Abstract

Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately evident that the method is fast and memory-efficient. Moreover, the method’s design is such that good convergence properties may be expected. In this paper, we commence a systematic investigation of these convergence properties.

Suggested Citation

  • Kai Diethelm, 2022. "A New Diffusive Representation for Fractional Derivatives, Part II: Convergence Analysis of the Numerical Scheme," Mathematics, MDPI, vol. 10(8), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1245-:d:790677
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    References listed on IDEAS

    as
    1. Roberto Garrappa, 2018. "Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial," Mathematics, MDPI, vol. 6(2), pages 1-23, January.
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