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	A parareal method for time-fractional differential equations
	Xu, Qinwu ; Hesthaven, Jan S. ; Chen, Feng
	2015
关键词	Fractional calculus Time-fractional Parareal Parallel-in-time Multi-domain spectral PARALLEL ALGORITHM DISCRETIZATION PDES
英文摘要	In this paper, a parareal method is proposed for the parallel-in-time integration of time-fractional differential equations (TFDEs). It is a generalization of the original parareal method, proposed for classic differential equations. To match the global feature of fractional derivatives, the new method has in the correction step embraced the history part of the solution. We provide a convergence analysis under the assumption of Lipschitz stability conditions. We use a multi-domain spectral integrator to build the serial solvers and numerical results demonstrate the feasibility of the new approach and confirm the convergence analysis. Studies also show that both the coarse resolution and the nature of the differential operators can affect the performance. (C) 2014 Elsevier Inc. All rights reserved.; Postdoctoral Science Foundation of China [2014M560839]; National Natural Science Foundation of China [51174236, 51134003]; NSF [DMS-1115416]; OSD/AFOSR [FA9550-09-1-0613]; AFOSR [FA9550-12-1-0463]; SCI(E); ARTICLE; xuqinwu@pku.edu.cn; jan.hesthaven@epfl.ch; feng.chen@baruch.cuny.edu; ,SI; 173-183; 293
语种	英语
出处	SCI
出版者	JOURNAL OF COMPUTATIONAL PHYSICS
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/418386]
专题	数学科学学院
推荐引用方式 GB/T 7714	Xu, Qinwu,Hesthaven, Jan S.,Chen, Feng. A parareal method for time-fractional differential equations. 2015-01-01.

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