A second-order scheme for a time-fractional diffusion equation

被引：5
|
作者：
Cen, Zhongdi [1 ]
Huang, Jian [1 ]
Le, Anbo [1 ]
Xu, Aimin [1 ]
机构：
[1] Zhejiang Wanli Univ, Inst Math, Ningbo, Zhejiang, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2019年 / 90卷
关键词：
Fractional differential equation; Caputo derivative; Singularity; Graded mesh;
D O I：
10.1016/j.aml.2018.10.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A reaction-diffusion problem with a Caputo time derivative is considered. An integral discretization scheme on a graded mesh along with a decomposition of the exact solution is proposed. It is shown that the scheme is second-order convergent, which exhibits an enhancement in the convergence rate compared with the L1 schemes. Numerical experiments are presented to support the theoretical result. (C) 2018 Elsevier Ltd. All rights reserved.
引用
收藏
页码：79 / 85
页数：7
相关论文
共 50 条
  • [41] A FAST HIGH ORDER METHOD FOR THE TIME-FRACTIONAL DIFFUSION EQUATION
    Zhu, Hongyi
    Xu, Chuanju
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2019, 57 (06) : 2829 - 2849
  • [42] Analysis of a Time-Fractional Substantial Diffusion Equation of Variable Order
    Zheng, Xiangcheng
    Wang, Hong
    Guo, Xu
    FRACTAL AND FRACTIONAL, 2022, 6 (02)
  • [43] A numerical method for the distributed order time-fractional diffusion equation
    Ford, Neville J.
    Morgado, M. Luisa
    Rebelo, Magda
    2014 INTERNATIONAL CONFERENCE ON FRACTIONAL DIFFERENTIATION AND ITS APPLICATIONS (ICFDA), 2014,
  • [44] A linearized second-order finite difference scheme for time fractional generalized BBM equation
    Lyu, Pin
    Vong, Seakweng
    APPLIED MATHEMATICS LETTERS, 2018, 78 : 16 - 23
  • [45] Time second-order splitting conservative difference scheme for nonlinear fractional Schrodinger equation
    Xie, Jianqiang
    Ali, Muhammad Aamir
    Zhang, Zhiyue
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (01) : 1411 - 1422
  • [46] Fast Iterative Method with a Second-Order Implicit Difference Scheme for Time-Space Fractional Convection–Diffusion Equation
    Xian-Ming Gu
    Ting-Zhu Huang
    Cui-Cui Ji
    Bruno Carpentieri
    Anatoly A. Alikhanov
    Journal of Scientific Computing, 2017, 72 : 957 - 985
  • [47] A second-order accurate numerical approximation for the fractional diffusion equation
    Tadjeran, C
    Meerschaert, MM
    Scheffler, HP
    JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 213 (01) : 205 - 213
  • [48] A Fast Second-Order ADI Finite Difference Scheme for the Two-Dimensional Time-Fractional Cattaneo Equation with Spatially Variable Coefficients
    Nong, Lijuan
    Yi, Qian
    Chen, An
    FRACTAL AND FRACTIONAL, 2024, 8 (08)
  • [49] Explicit Chebyshev-Galerkin scheme for the time-fractional diffusion equation
    Moustafa, M.
    Youssri, Y. H.
    Atta, A. G.
    INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2024, 35 (01):
  • [50] A difference scheme for the time-fractional diffusion equation on a metric star graph
    Mehandiratta, Vaibhav
    Mehra, Mani
    APPLIED NUMERICAL MATHEMATICS, 2020, 158 (158) : 152 - 163
12345