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An efficient parallel algorithm for the numerical solution of fractional differential equations. (English) Zbl 1273.65101

Summary: 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.

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A08 Fractional ordinary differential equations
65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
65Y05 Parallel numerical computation
68W10 Parallel algorithms in computer science

Software:

RODAS; Scalasca; VAMPIR
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References:

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