A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations

被引：4
|
作者：
Arshad, Sadia [1 ,4 ]
Baleanu, Dumitru [2 ,6 ,7 ]
Huang, Jianfei [3 ]
Tang, Yifa [4 ,5 ]
Zhao, Yue [4 ,5 ]
机构：
[1] COMSATS Univ Islamabad, Lahore, Pakistan
[2] Cankaya Univ, Dept Math, TR-06530 Ankara, Turkey
[3] Yangzhou Univ, Coll Math Sci, Yangzhou 225002, Jiangsu, Peoples R China
[4] Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
[5] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
[6] Inst Space Sci, Magurele 077125, Romania
[7] Tshwane Univ Technol, Fac Sci, Dept Math & Stat, Arcadia Campus,Bldg 2-117,Nelson Mandela Dr, ZA-0001 Pretoria, South Africa
来源：
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2018年 / 8卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Fractional diffusion equation; Riesz derivative; high-order approximation; stability; convergence; IMPLICIT NUMERICAL-METHOD; HIGH-ORDER APPROXIMATION; SPECTRAL METHOD; CAPUTO DERIVATIVES; SCHEME; CONVERGENCE;
D O I：
10.4208/eajam.280218.210518
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A finite difference method for a class of time-space fractional diffusion equations is considered. The trapezoidal formula and a fourth-order fractional compact difference scheme are, respectively, used in temporal and spatial discretisations and the method stability is studied. Theoretical estimates of the convergence in the L-2 -norm are shown to be O(tau(2) + h(4)), where tau and h are time and space mesh sizes. Numerical examples confirm theoretical results.
引用
收藏
页码：764 / 781
页数：18
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