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
  • [41] The characteristic difference DDM for solving the time-fractional order convection–diffusion equations
    Zhongguo Zhou
    Ning Wang
    Hao Pan
    Yan Wang
    Computational and Applied Mathematics, 2023, 42
  • [42] An α-robust finite difference method for a time-fractional radially symmetric diffusion problem
    Wang, Lin
    Stynes, Martin
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2021, 97 : 386 - 393
  • [43] A weak Galerkin/finite difference method for time-fractional biharmonic problems in two dimensions
    Yazdani, A.
    Momeni, H.
    Cheichan, M. S.
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 410
  • [44] A Characteristic Difference Scheme for Time-Fractional Heat Equations Based on the Crank-Nicholson Difference Schemes
    Karatay, Ibrahim
    Bayramoglu, Serife R.
    ABSTRACT AND APPLIED ANALYSIS, 2012,
  • [45] Three-point combined compact difference schemes for time-fractional advection-diffusion equations with smooth solutions
    Gao, Guang-Hua
    Sun, Hai-Wei
    JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 298 : 520 - 538
  • [46] Finite difference scheme for the time-space fractional diffusion equations
    Cao, Jianxiong
    Li, Changpin
    CENTRAL EUROPEAN JOURNAL OF PHYSICS, 2013, 11 (10): : 1440 - 1456
  • [47] Two finite difference schemes for time fractional diffusion-wave equation
    Jianfei Huang
    Yifa Tang
    Luis Vázquez
    Jiye Yang
    Numerical Algorithms, 2013, 64 : 707 - 720
  • [48] An implicit difference scheme for time-fractional diffusion equations with a time-invariant type variable order
    Gu, Xian-Ming
    Sun, Hai-Wei
    Zhao, Yong-Liang
    Zheng, Xiangcheng
    APPLIED MATHEMATICS LETTERS, 2021, 120
  • [49] A class of time-fractional diffusion equations with generalized fractional derivatives
    Alikhanov, Anatoly A.
    Huang, Chengming
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 414
  • [50] Two finite difference schemes for time fractional diffusion-wave equation
    Huang, Jianfei
    Tang, Yifa
    Vazquez, Luis
    Yang, Jiye
    NUMERICAL ALGORITHMS, 2013, 64 (04) : 707 - 720
12345