Stationary iterated weighted Tikhonov regularization method for identifying an unknown source term of time-fractional radial heat equation

被引：2
|
作者：
Yang, Shuping [1 ]
Xiong, Xiangtuan [2 ]
Pan, Ping [1 ]
Sun, Yue [1 ]
机构：
[1] Shaanxi Univ Technol, Dept Math, Hanzhong, Peoples R China
[2] Northwest Normal Univ, Dept Math, Lanzhou, Peoples R China
来源：
NUMERICAL ALGORITHMS | 2022年 / 90卷 / 02期
关键词：
Inverse source problem; Stationary iterated weighted Tikhonov; Error estimate; INVERSE SOURCE PROBLEM; DIFFUSION EQUATION;
D O I：
10.1007/s11075-021-01213-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The ill-posed problem of unknown source identification in the time-fractional radial heat conduction equation is studied. In order to overcome the ill-posedness of the problem, a stationary iterated weighted Tikhonov regularization method is proposed. The a-priori and the a-posteriori choice rules for regularization parameters are discussed and the corresponding convergence rates of both are obtained. The stationary iterated weighted Tikhonov regularization method goes beyond the saturation results of weighted Tikhonov regularization method. A numerical example shows the effectiveness of this method.
引用
收藏
页码：881 / 903
页数：23
相关论文
共 50 条
  • [21] The fractional Tikhonov regularization methods for identifying the initial value problem for a time-fractional diffusion equation
    Yang, Fan
    Pu, Qu
    Li, Xiao-Xiao
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 380
  • [22] The Simplified Tikhonov Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation
    Yang, Fan
    Guo, HengZhen
    Li, XiaoXiao
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2011, 2011
  • [23] Identifying an unknown source in the Poisson equation by the method of Tikhonov regularization in Hilbert scales
    Zhao, Zhenyu
    Meng, Zehong
    You, Lei
    Xie, Ou
    APPLIED MATHEMATICAL MODELLING, 2014, 38 (19-20) : 4686 - 4693
  • [24] Tikhonov regularization method for a backward problem for the inhomogeneous time-fractional diffusion equation
    Nguyen Huy Tuan
    Le Dinh Long
    Tatar, Salih
    APPLICABLE ANALYSIS, 2018, 97 (05) : 842 - 863
  • [25] Optimal error bound and generalized Tikhonov regularization for identifying an unknown source in the heat equation
    Qian, Ailin
    Li, Yan
    JOURNAL OF MATHEMATICAL CHEMISTRY, 2011, 49 (03) : 765 - 775
  • [26] Optimal error bound and generalized Tikhonov regularization for identifying an unknown source in the heat equation
    Ailin Qian
    Yan Li
    Journal of Mathematical Chemistry, 2011, 49 : 765 - 775
  • [27] Tikhonov regularization for simultaneous inversion of initial value and source term of a time-fractional Black-Scholes equation
    Wu, Hanghang
    Yang, Hongqi
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024,
  • [28] A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation
    Gao, Jinghuai
    Wang, Dehua
    Peng, Jigen
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2012, 2012
  • [29] Tikhonov-type regularization method for a sideways problem of the time-fractional diffusion equation
    Zhang, Hongwu
    Zhang, Xiaoju
    AIMS MATHEMATICS, 2021, 6 (01): : 90 - 101
  • [30] A modified Tikhonov regularization for unknown source in space fractional diffusion equation
    Yu, Kai
    Gong, Benxue
    Zhao, Zhenyu
    OPEN MATHEMATICS, 2022, 20 (01): : 1309 - 1319
12345