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	A multi-domain spectral method for time-fractional differential equations
	Chen, Feng ; Xu, Qinwu ; Hesthaven, Jan S.
	2015
关键词	Multi-domain Spectral Time-fractional High-order integration Three-term-recurrence General linear method GINZBURG-LANDAU EQUATION DIFFUSION-EQUATIONS ELEMENT METHODS APPROXIMATIONS
英文摘要	This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations. (C) 2014 Elsevier Inc. All rights reserved.; OSD/AFOSR [FA9550-09-1-0613]; AFOSR [FA9550-12-1-0463]; Postdoctoral Science Foundation of China [2014M560839]; National Natural Science Foundation of China [51174236, 51134003]; NSF [DMS-1115416]; SCI(E); ARTICLE; feng.chen@baruch.cuny.edu; qw_xu@hotmail.com; jan.hesthaven@epfl.ch; ,SI; 157-172; 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/20.500.11897/418385]
专题	数学科学学院
推荐引用方式 GB/T 7714	Chen, Feng,Xu, Qinwu,Hesthaven, Jan S.. A multi-domain spectral method for time-fractional differential equations. 2015-01-01.

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