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

被引：3
|
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
相关论文
共 50 条
  • [31] A fourth-order scheme for space fractional diffusion equations
    Guo, Xu
    Li, Yutian
    Wang, Hong
    JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 373 : 410 - 424
  • [32] FOURTH ORDER ACCURATE SCHEME FOR THE SPACE FRACTIONAL DIFFUSION EQUATIONS
    Chen, Minghua
    Deng, Weihua
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2014, 52 (03) : 1418 - 1438
  • [33] A COMPACT FINITE DIFFERENCE SCHEME FOR SPACE-TIME FRACTIONAL DIFFUSION EQUATIONS WITH TIME DISTRIBUTED-ORDER DERIVATIVE
    Feng, Qinghua
    UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2018, 80 (04): : 79 - 90
  • [34] Finite difference/finite element method for a nonlinear time-fractional fourth-order reaction-diffusion problem
    Liu, Yang
    Du, Yanwei
    Li, Hong
    He, Siriguleng
    Gao, Wei
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2015, 70 (04) : 573 - 591
  • [35] A NOTE ON THE STABILITY OF A SECOND ORDER FINITE DIFFERENCE SCHEME FOR SPACE FRACTIONAL DIFFUSION EQUATIONS
    Qu, Wei
    Lei, Siu-Long
    Vong, Seak-Weng
    NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION, 2014, 4 (04): : 317 - 325
  • [36] Block preconditioning strategies for time-space fractional diffusion equations
    Chen, Hao
    Zhang, Tongtong
    Lv, Wen
    APPLIED MATHEMATICS AND COMPUTATION, 2018, 337 : 41 - 53
  • [37] Block splitting preconditioner for time-space fractional diffusion equations
    Luo, Jia-Min
    Li, Hou-Biao
    Wei, Wei-Bo
    ELECTRONIC RESEARCH ARCHIVE, 2022, 30 (03): : 780 - 797
  • [38] Numerical analysis of a fourth-order linearized difference method for nonlinear time-space fractional Ginzburg-Landau equation
    Fei, Mingfa
    Li, Wenhao
    Yi, Yulian
    ELECTRONIC RESEARCH ARCHIVE, 2022, 30 (10): : 3635 - 3659
  • [39] Fractional difference/finite element approximations for the time-space fractional telegraph equation
    Zhao, Zhengang
    Li, Changpin
    APPLIED MATHEMATICS AND COMPUTATION, 2012, 219 (06) : 2975 - 2988
  • [40] Efficient difference method for time-space fractional diffusion equation with Robin fractional derivative boundary condition
    Biao Zhang
    Weiping Bu
    Aiguo Xiao
    Numerical Algorithms, 2021, 88 : 1965 - 1988
12345