Fast Finite Difference Schemes for Time-Fractional Diffusion Equations with a Weak Singularity at Initial Time

被引：49
|
作者：
Shen, Jin-ye [1 ]
Sun, Zhi-zhong [1 ]
Du, Rui [1 ]
机构：
[1] Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China
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 differential equation; difference scheme; fast algorithm; singularity; NONUNIFORM TIMESTEPS; STEPPING METHOD; DYNAMICS; MESHES;
D O I：
10.4208/eajam.010418.020718
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A sharp estimate for the L1 formula on graded meshes, which approximates the Caputo derivatives of functions with a weak singularity at t = 0 is obtained. Combining such approximations with the sum-of-exponential approximations of the kernel, we develop fast difference schemes for one- and two-dimensional fractional diffusion equations, the solutions of which have a weak singularity at the starting time. The proof of the stability and convergence is based on the maximum principle. Numerical examples confirm theoretical estimates.
引用
收藏
页码：834 / 858
页数：25
相关论文
共 50 条
  • [1] Second order difference schemes for time-fractional KdVBurgers equation with initial singularity
    Cen, Dakang
    Wang, Zhibo
    Mo, Yan
    Applied Mathematics Letters, 2021, 112
  • [2] Second order difference schemes for time-fractional KdV-Burgers' equation with initial singularity
    Cen, Dakang
    Wang, Zhibo
    Mo, Yan
    APPLIED MATHEMATICS LETTERS, 2021, 112
  • [3] Temporal Second-Order Fast Finite Difference/Compact Difference Schemes for Time-Fractional Generalized Burgers' Equations
    Peng, Xiangyi
    Qiu, Wenlin
    Hendy, Ahmed S.
    Zaky, Mahmoud A.
    JOURNAL OF SCIENTIFIC COMPUTING, 2024, 99 (02)
  • [4] Finite difference schemes for time-fractional Schrodinger equations via fractional linear multistep method
    Hicdurmaz, Betul
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2021, 98 (08) : 1561 - 1573
  • [5] A fast difference scheme for the variable coefficient time-fractional diffusion wave equations
    Ran, Maohua
    Lei, Xiaojuan
    APPLIED NUMERICAL MATHEMATICS, 2021, 167 : 31 - 44
  • [6] Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations
    Zeng, Fanhai
    Zhang, Zhongqiang
    Karniadakis, George Em
    JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 307 : 15 - 33
  • [7] A Family of Transformed Difference Schemes for Nonlinear Time-Fractional Equations
    Qin, Hongyu
    Chen, Xiaoli
    Zhou, Boya
    FRACTAL AND FRACTIONAL, 2023, 7 (01)
  • [8] Higher order numerical approximations for non-linear time-fractional reaction–diffusion equations exhibiting weak initial singularity
    Singh, Anshima
    Kumar, Sunil
    Communications in Nonlinear Science and Numerical Simulation, 2024, 139
  • [9] Stability and convergence of finite difference schemes for a class of time-fractional sub-diffusion equations based on certain superconvergence
    Gao, Guang-Hua
    Sun, Hai-Wei
    Sun, Zhi-Zhong
    JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 280 : 510 - 528
  • [10] Finite difference schemes for the two-dimensional multi-term time-fractional diffusion equations with variable coefficients
    Mingrong Cui
    Computational and Applied Mathematics, 2021, 40
12345