A Generalized Iterated Tikhonov Method in the Fourier Domain for Determining the Unknown Source of the Time-Fractional Diffusion Equation

In this paper, an inverse problem of determining a source in a time-fractional diffusion equation is investigated. A Fourier extension scheme is used to approximate the solution to avoid the impact on smoothness caused by directly using singular system eigenfunctions for approximation. A modified im...

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Bibliographic Details
Published in:Symmetry (Basel) 2024-07, Vol.16 (7), p.864
Main Authors: Zheng, Bin, Liu, Junfeng, Zhao, Zhenyu, Dou, Zhihong, Gong, Benxue
Format: Article
Language:English
Subjects:
Accuracy
Approximation
Boundary conditions
Diffusion rate
discrepancy principle
Eigenvectors
Fourier extension
generalized iterated Tikhonov method
ill-posed problem
Inverse problems
Iterative methods
Parameter modification
Regularization
Regularization methods
Smoothness
unknown source
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Summary:In this paper, an inverse problem of determining a source in a time-fractional diffusion equation is investigated. A Fourier extension scheme is used to approximate the solution to avoid the impact on smoothness caused by directly using singular system eigenfunctions for approximation. A modified implicit iteration method is proposed as a regularization technique to stabilize the solution process. The convergence rates are derived when a discrepancy principle serves as the principle for choosing the regularization parameters. Numerical tests are provided to further verify the efficacy of the proposed method.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym16070864