A numerical method for solving retrospective inverse problem of fractional parabolic equation

被引：4
|
作者：
Su, Lingde [1 ,4 ]
Huang, Jian [2 ,3 ]
Vasil'ev, V. I. [4 ]
Li, Ao [2 ,3 ]
Kardashevsky, A. M. [4 ]
机构：
[1] Zaozhuang Univ, Sch Math & Stat, Zaozhuang, Shandong, Peoples R China
[2] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan, Peoples R China
[3] Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan, Peoples R China
[4] North Eastern Fed Univ, Inst Math & Informat Sci, Yakutsk, Republic Of Sak, Russia
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 413卷
基金：
中国国家自然科学基金; 俄罗斯科学基金会;
关键词：
Time fractional parabolic equation; Inverse problem; Caputo fractional derivatives; Ill-posed problems; Conjugate gradients method; SAVITZKY-GOLAY; HEAT-LIKE; DIFFUSION; APPROXIMATE; COEFFICIENT;
D O I：
10.1016/j.cam.2022.114366
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An effective numerical method for solving the inverse problem of time fractional parabolic equation is constructed in this paper. We use implicit finite difference method to discretize the problem and for the inverse problem we propose a conjugate gradient type regularization method to solve the discretized ill-posed linear systems. By comparing the different errors and the results with different perturbed data in several numerical experiments, our method is shown to solve the inverse problem, even with some noisy measurements, efficiently and stably. (c) 2022 Elsevier B.V. All rights reserved.
引用
收藏
页数：11
相关论文
共 50 条
  • [31] Comparing numerical methods for inverse coefficient problem in parabolic equation
    Fatullayev, Afet Golayoglu
    Can, Emine
    Gasilov, Nizami
    APPLIED MATHEMATICS AND COMPUTATION, 2006, 179 (02) : 567 - 571
  • [32] Numerical simulation for an inverse source problem in a degenerate parabolic equation
    Rao, Xiao-Bo
    Wang, Yu-Xin
    Qian, Kun
    Deng, Zui-Cha
    Yang, Liu
    APPLIED MATHEMATICAL MODELLING, 2015, 39 (23-24) : 7537 - 7553
  • [33] Numerical Solution of the Retrospective Inverse Parabolic Problem on Disjoint Intervals
    Koleva, Miglena N.
    Vulkov, Lubin G.
    COMPUTATION, 2023, 11 (10)
  • [34] Solving the inverse problem of identifying an unknown source term in a parabolic equation
    Shidfar, A.
    Babaei, A.
    Molabahrami, A.
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 60 (05) : 1209 - 1213
  • [35] On an inverse problem of the Bitsadze–Samarskii type for a parabolic equation of fractional order
    Ravshan Ashurov
    Baxtiyar Kadirkulov
    Muhammadali Jalilov
    Boletín de la Sociedad Matemática Mexicana, 2023, 29
  • [36] Inverse Problem for a Time Fractional Parabolic Equation with Nonlocal Boundary Conditions
    Ozbilge, Ebru
    Kanca, Fatma
    Ozbilge, Emre
    MATHEMATICS, 2022, 10 (09)
  • [37] INVERSE PROBLEM FOR FRACTIONAL ORDER PSEUDO-PARABOLIC EQUATION WITH INVOLUTION
    Serikbaev, D.
    UFA MATHEMATICAL JOURNAL, 2020, 12 (04): : 119 - 135
  • [38] INVERSE PROBLEM FOR A PARABOLIC EQUATION
    SHISHKO, NP
    MATHEMATICAL NOTES, 1981, 29 (1-2) : 28 - 32
  • [39] On an Inverse Problem for a Parabolic Equation
    D. S. Tkachenko
    Mathematical Notes, 2004, 75 : 676 - 689
  • [40] On an inverse problem for a parabolic equation
    Tkachenko, DS
    MATHEMATICAL NOTES, 2004, 75 (5-6) : 676 - 689
12345