A Truncation Method Based on Hermite Expansion for Unknown Source in Space Fractional Diffusion Equation

被引：4
|
作者：
Zhao, Zhenyu [1 ]
Xie, Ou [1 ]
You, Lei [1 ]
Meng, Zehong [2 ]
机构：
[1] Guangdong Ocean Univ, Coll Sci, Zhanjiang 524088, Peoples R China
[2] Zhejiang Univ Finance & Econ, Sch Math & Stat, Hangzhou 310018, Zhejiang, Peoples R China
来源：
MATHEMATICAL MODELLING AND ANALYSIS | 2014年 / 19卷 / 03期
基金：
中国国家自然科学基金;
关键词：
ill-posed problem; unknown source; truncation method; Hermite functions expansion; discrepancy principle; SIDEWAYS HEAT-EQUATION; REGULARIZATION METHODS; DYNAMICS; WAVELET;
D O I：
10.3846/13926292.2014.929057
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we consider the problem for identifying an unknown steady source in a space fractional diffusion equation. A truncation method based on a Hermite function expansion is proposed, and the regularization parameter is chosen by a discrepancy principle. An error estimate between the exact solution and its approximation is given. A numerical implementation is discussed and corresponding results are presented to verify the effectiveness of the method.
引用
收藏
页码：430 / 442
页数：13
相关论文
共 50 条
  • [41] Inverse source problem for a space-time fractional diffusion equation
    Mohamed BenSaleh
    Hassine Maatoug
    Ricerche di Matematica, 2024, 73 : 681 - 713
  • [42] Inverse source problem for a space-time fractional diffusion equation
    BenSaleh, Mohamed
    Maatoug, Hassine
    RICERCHE DI MATEMATICA, 2024, 73 (02) : 681 - 713
  • [43] INVERSE SOURCE PROBLEM FOR A SPACE-TIME FRACTIONAL DIFFUSION EQUATION
    Ali, Muhammad
    Aziz, Sara
    Malik, Salman A.
    FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2018, 21 (03) : 844 - 863
  • [44] Optimization method for determining the source term in fractional diffusion equation
    Ma, Yong-Ki
    Prakash, P.
    Deiveegan, A.
    MATHEMATICS AND COMPUTERS IN SIMULATION, 2019, 155 : 168 - 176
  • [45] A New Numerical Method for the Riesz Space Fractional Diffusion Equation
    Ding, Heng-fei
    Zhang, Yu-xin
    He, Wan-sheng
    Yang, Xiao-ya
    ADVANCED MATERIALS RESEARCH, 2011, 213 : 393 - 396
  • [46] The Space-Time Spectral Method for a Fractional Diffusion Equation
    Huang, Yu
    PROCEEDINGS OF THE 2010 INTERNATIONAL CONFERENCE ON APPLICATION OF MATHEMATICS AND PHYSICS, VOL 2: ADVANCES ON APPLIED MATHEMATICS AND COMPUTATION MATHEMATICS, 2010, : 347 - 350
  • [47] An Efficient Space–Time Method for Time Fractional Diffusion Equation
    Jie Shen
    Chang-Tao Sheng
    Journal of Scientific Computing, 2019, 81 : 1088 - 1110
  • [48] Identifying the space source term problem for time-space-fractional diffusion equation
    Karapinar, Erdal
    Kumar, Devendra
    Sakthivel, Rathinasamy
    Nguyen Hoang Luc
    Can, N. H.
    ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
  • [49] Identifying the space source term problem for time-space-fractional diffusion equation
    Erdal Karapinar
    Devendra Kumar
    Rathinasamy Sakthivel
    Nguyen Hoang Luc
    N. H. Can
    Advances in Difference Equations, 2020
  • [50] The solution of the time-space fractional diffusion equation based on the Chebyshev collocation method
    Duan, Junsheng
    Jing, Lixia
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2023,
12345