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 | |
![]() |
【 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.
【 授权许可】
Free
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
10_1016_j_jcp_2014_10_016.pdf | 1432KB | ![]() |