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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:
65L06Multistep, Runge-Kutta, and extrapolation methods
34A08Fractional differential equations
65R20Integral equations (numerical methods)
45J05Integro-ordinary differential equations
65Y05Parallel computation (numerical methods)
68W10Parallel algorithms