期刊论文详细信息
JOURNAL OF COMPUTATIONAL PHYSICS 卷:293
A multi-domain spectral method for time-fractional differential equations
Article
Chen, Feng1  Xu, Qinwu2,3  Hesthaven, Jan S.4 
[1] CUNY Bernard M Baruch Coll, Dept Math, New York, NY 10010 USA
[2] Peking Univ, Sch Math Sci, Beijing, Peoples R China
[3] Cent S Univ, Sch Math & Stat, Changsha, Hunan, Peoples R China
[4] Ecole Polytech Fed Lausanne, EPFL SB MATHICSE MCSS, CH-1015 Lausanne, Switzerland
关键词: Multi-domain;    Spectral;    Time-fractional;    High-order integration;    Three-term-recurrence;    General linear method;   
DOI  :  10.1016/j.jcp.2014.10.016
来源: Elsevier
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【 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.

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