A high-order spectral method for the multi-term time-fractional diffusion equations

被引：131
|
作者：
Zheng, M. [1 ]
Liu, F. [2 ]
Anh, V. [2 ]
Turner, I. [2 ]
机构：
[1] Huzhou Univ, Sch Math Sci, Huzhou 313000, Peoples R China
[2] Queensland Univ Technol, Sch Math Sci, GPO Box 2434, Brisbane, Qld 4001, Australia
来源：
APPLIED MATHEMATICAL MODELLING | 2016年 / 40卷 / 7-8期
关键词：
Multi-term time-fractional diffusion equation; Space-time spectral method; Riemann-Liouville derivative; Caputo fractional derivative; BOUNDARY-VALUE-PROBLEMS; VARIABLE-ORDER; SPACE; APPROXIMATIONS;
D O I：
10.1016/j.apm.2015.12.011
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
The multi-term time-fractional diffusion equation is a useful tool in the modeling of complex systems. This paper aims to develop a high order numerical method for solving multi term time-fractional diffusion equations. Based on the space-time spectral method, a high order scheme is proposed in the present paper. In this method, the Legendre polynomials are adopted in temporal discretization and the Fourier-like basis functions are constructed for the spatial discretization. Such a space-time spectral method possesses high efficiency and exponential decay in both time and space directions. Rigorous proofs are given here for the stability and convergence of the scheme. Numerical results show good agreement with the theoretical analysis. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：4970 / 4985
页数：16
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