Finite difference scheme for multi-term variable-order fractional diffusion equation

被引:17
|
作者
Xu, Tao [1 ]
Lu, Shujuan [1 ]
Chen, Wenping [1 ]
Chen, Hu [1 ]
机构
[1] Beihang Univ, Sch Math & Syst Sci, Beijing, Peoples R China
基金
中国国家自然科学基金;
关键词
Multi-term fractional diffusion equation; Variable-order fractional derivatives; Difference scheme; Stability; Convergence;
D O I
10.1186/s13662-018-1544-8
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we consider a multi-term variable-order fractional diffusion equation on a finite domain, which involves the Caputo variable-order time fractional derivative of order alpha(x, t) is an element of (0, 1) and the Riesz variable-order space fractional derivatives of order beta(x, t) is an element of(0, 1), gamma (x, t) is an element of(1, 2). Approximating the temporal direction derivative by L1-algorithm and the spatial direction derivative by the standard and shifted Grunwald method, respectively, a characteristic finite difference scheme is proposed. The stability and convergence of the difference schemes are analyzed via mathematical induction. Some numerical experiments are provided to show the efficiency of the proposed difference schemes.
引用
收藏
页数:13
相关论文
共 50 条
  • [1] Finite difference scheme for multi-term variable-order fractional diffusion equation
    Tao Xu
    Shujuan Lü
    Wenping Chen
    Hu Chen
    [J]. Advances in Difference Equations, 2018
  • [2] Local discontinuous Galerkin method for multi-term variable-order time fractional diffusion equation
    Wei, Leilei
    Wang, Huanhuan
    [J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2023, 203 : 685 - 698
  • [3] ANALYSIS OF A MULTI-TERM VARIABLE-ORDER TIME-FRACTIONAL DIFFUSION EQUATION AND ITS GALERKIN FINITE ELEMENT APPROXIMATION
    Liu, Huan
    Null, Xiangcheng Zheng
    Fu, Hongfei
    [J]. JOURNAL OF COMPUTATIONAL MATHEMATICS, 2022, 40 (05) : 818 - 838
  • [4] FINITE DIFFERENCE SCHEMES FOR VARIABLE-ORDER TIME FRACTIONAL DIFFUSION EQUATION
    Sun, Hongguang
    Chen, Wen
    Li, Changpin
    Chen, Yangquan
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2012, 22 (04):
  • [5] A wavelet approach for solving multi-term variable-order time fractional diffusion-wave equation
    Heydari, Mohammad Hossein
    Avazzadeh, Zakieh
    Haromi, Malih Farzi
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2019, 341 : 215 - 228
  • [6] Efficient finite difference scheme for a hidden-memory variable-order time-fractional diffusion equation
    Sun L.-Y.
    Lei S.-L.
    Sun H.-W.
    [J]. Computational and Applied Mathematics, 2023, 42 (08)
  • [7] Finite difference/collocation method to solve multi term variable-order fractional reaction-advection-diffusion equation in heterogeneous medium
    Dwivedi, Kushal Dhar
    Rajeev
    Das, S.
    Gomez-Aguilar, Jose Francisco
    [J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2021, 37 (03) : 2031 - 2045
  • [8] MAXIMUM PRINCIPLES FOR MULTI-TERM SPACE-TIME VARIABLE-ORDER FRACTIONAL DIFFUSION EQUATIONS AND THEIR APPLICATIONS
    Liu, Zhenhai
    Zeng, Shengda
    Bai, Yunru
    [J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2016, 19 (01) : 188 - 211
  • [9] Maximum Principles for Multi-Term Space-Time Variable-Order Fractional Diffusion Equations and their Applications
    Liu Zhenhai
    Zeng Shengda
    Bai Yunru
    [J]. Fractional Calculus and Applied Analysis, 2016, 19 : 188 - 211
  • [10] Discrete comparison principle of a finite difference method for the multi-term time fractional diffusion equation
    Yue Wang
    Youxing Zhao
    Hu Chen
    [J]. Numerical Algorithms, 2023, 93 : 1581 - 1593