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An efficient parallel algorithm for the numerical solution of fractional differential equations

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Abstract

The numerical solution of differential equations of fractional order is known to be a computationally very expensive problem due to the nonlocal nature of the fractional differential operators. We demonstrate that parallelization may be used to overcome these difficulties. To this end we propose to implement the fractional version of the second-order Adams-Bashforth-Moulton method on a parallel computer. According to many recent publications, this algorithm has been successfully applied to a large number of fractional differential equations arising from a variety of application areas. The precise nature of the parallelization concept is discussed in detail and some examples are given to show the viability of our approach.

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Authors and Affiliations

  1. GNS Gesellschaft für numerische Simulation mbH, Am Gaußberg 2, 38114, Braunschweig, Germany

    Kai Diethelm

  2. Institut Computational Mathematics, Technische Universität Braunschweig, Pockelsstr. 14, 38106, Braunschweig, Germany

    Kai Diethelm

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  1. Kai Diethelm
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Correspondence to Kai Diethelm.

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Diethelm, K. An efficient parallel algorithm for the numerical solution of fractional differential equations. fcaa 14, 475–490 (2011). https://doi.org/10.2478/s13540-011-0029-1

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  • DOI: https://doi.org/10.2478/s13540-011-0029-1

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