Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation

被引：278
|
作者：
Wang, Zhibo [1 ]
Vong, Seakweng [1 ]
机构：
[1] Univ Macau, Dept Math, Taipa, Macau, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL PHYSICS | 2014年 / 277卷
关键词：
Modified anomalous fractional sub-diffusion equation; Fractional diffusion-wave equation; Compact difference scheme; Weighted and shifted Grunwald difference operator; NEUMANN BOUNDARY-CONDITIONS; HIGH SPATIAL ACCURACY; NONLINEAR SOURCE-TERM; SUBDIFFUSION EQUATION; NUMERICAL-METHODS; HIGH-ORDER; APPROXIMATIONS; STABILITY; ALGORITHM;
D O I：
10.1016/j.jcp.2014.08.012
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this paper, compact finite difference schemes for the modified anomalous fractional sub-diffusion equation and fractional diffusion-wave equation are studied. Schemes proposed previously can at most achieve temporal accuracy of order which depends on the order of fractional derivatives in the equations and is usually less than two. Based on the idea of weighted and shifted Grunwald difference operator, we establish schemes with temporal and spatial accuracy order equal to two and four respectively. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：1 / 15
页数：15
相关论文
共 50 条
  • [1] A compact difference scheme for the fractional diffusion-wave equation
    Du, R.
    Cao, W. R.
    Sun, Z. Z.
    [J]. APPLIED MATHEMATICAL MODELLING, 2010, 34 (10) : 2998 - 3007
  • [2] Modified implicit fractional difference scheme for 2D modified anomalous fractional sub-diffusion equation
    Ali, Umair
    Abdullah, Farah Aini
    Mohyud-Din, Syed Tauseef
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2017,
  • [3] Modified implicit fractional difference scheme for 2D modified anomalous fractional sub-diffusion equation
    Umair Ali
    Farah Aini Abdullah
    Syed Tauseef Mohyud-Din
    [J]. Advances in Difference Equations, 2017
  • [4] Temporal second-order difference schemes for the nonlinear time-fractional mixed sub-diffusion and diffusion-wave equation with delay
    Alikhanov, Anatoly A.
    Asl, Mohammad Shahbazi
    Huang, Chengming
    Apekov, Aslan M.
    [J]. PHYSICA D-NONLINEAR PHENOMENA, 2024, 464
  • [5] Two finite difference schemes for time fractional diffusion-wave equation
    Huang, Jianfei
    Tang, Yifa
    Vazquez, Luis
    Yang, Jiye
    [J]. NUMERICAL ALGORITHMS, 2013, 64 (04) : 707 - 720
  • [6] Two finite difference schemes for time fractional diffusion-wave equation
    Jianfei Huang
    Yifa Tang
    Luis Vázquez
    Jiye Yang
    [J]. Numerical Algorithms, 2013, 64 : 707 - 720
  • [7] Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions
    Ren, Jincheng
    Sun, Zhi-Zhong
    Zhao, Xuan
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 232 (01) : 456 - 467
  • [8] Compact implicit difference approximation for time-fractional diffusion-wave equation
    Ali, Umair
    Iqbal, Azhar
    Sohail, Muhammad
    Abdullah, Farah Aini
    Khan, Zohaib
    [J]. ALEXANDRIA ENGINEERING JOURNAL, 2022, 61 (05) : 4119 - 4126
  • [9] Stability analysis of a second-order difference scheme for the time-fractional mixed sub-diffusion and diffusion-wave equation
    Alikhanov, Anatoly A.
    Asl, Mohammad Shahbazi
    Huang, Chengming
    [J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2024, 27 (01) : 102 - 123
  • [10] Stability analysis of a second-order difference scheme for the time-fractional mixed sub-diffusion and diffusion-wave equation
    Anatoly A. Alikhanov
    Mohammad Shahbazi Asl
    Chengming Huang
    [J]. Fractional Calculus and Applied Analysis, 2024, 27 : 102 - 123
12345