High Accuracy Spectral Method for the Space-Fractional Diffusion Equations

被引：14
|
作者：
Zhai, Shuying [1 ]
Gui, Dongwei [2 ]
Zhao, Jianping [3 ]
Feng, Xinlong [3 ]
机构：
[1] Huaqiao Univ, Sch Math Sci, Quanzhou 362011, Peoples R China
[2] Chinese Acad Sci, Xinjiang Inst Ecol & Geog, Cele Natl Stn Observat & Res Desert Grassland Eco, Urumqi, Xinjiang, Peoples R China
[3] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China
来源：
JOURNAL OF MATHEMATICAL STUDY | 2014年 / 47卷 / 03期
关键词：
Space-fractional diffusion equation; fractional Laplacian; Chebyshev collocation method; Fourier spectral method; implicit-explicit Runge-Kutta method;
D O I：
10.4208/jms.v47n3.14.03
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, a high order accurate spectral method is presented for the space-fractional diffusion equations. Based on Fourier spectral method in space and Chebyshev collocation method in time, three high order accuracy schemes are proposed. Themain advantages of this method are that it yields a fully diagonal representation of the fractional operator, with increased accuracy and efficiency comparedwith low-order counterparts, and a completely straightforward extension to high spatial dimensions. Some numerical examples, including Allen-Cahn equation, are conducted to verify the effectiveness of this method.
引用
收藏
页码：274 / 286
页数：13
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