Exponential Tikhonov Regularization Method for Solving an Inverse Source Problem of Time Fractional Diffusion Equation
Year: 2023
Author: Zewen Wang, Shufang Qiu, Shuang Yu, Bin Wu, Wen Zhang
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 2 : pp. 173–190
Abstract
In this paper, we mainly study an inverse source problem of time fractional diffusion equation in a bounded domain with an over-specified terminal condition at a fixed time. A novel regularization method, which we call the exponential Tikhonov regularization method with a parameter $\gamma$, is proposed to solve the inverse source problem, and the corresponding convergence analysis is given under a-priori and a-posteriori regularization parameter choice rules. When $\gamma$ is less than or equal to zero, the optimal convergence rate can be achieved and it is independent of the value of $\gamma$. However, when $\gamma$ is greater than zero, the optimal convergence rate depends on the value of $\gamma$ which is related to the regularity of the unknown source. Finally, numerical experiments are conducted for showing the effectiveness of the proposed exponential regularization method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2107-m2020-0133
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 2 : pp. 173–190
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Exponential regularization method Inverse source problem Fractional diffusion equation Ill-posed problem Convergence rate.
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