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

被引:0
作者
Kai Diethelm
机构
[1] GNS Gesellschaft für numerische Simulation mbH,Institut Computational Mathematics
[2] Technische Universität Braunschweig,undefined
来源
Fractional Calculus and Applied Analysis | 2011年 / 14卷
关键词
fractional differential equation; numerical solution; Adams-Bashforth-Moulton method; parallel algorithm; Primary 65Y05; Secondary 65L05, 65R20;
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学科分类号
摘要
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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页码:475 / 490
页数:15
相关论文
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