@Article{JCM-41-2,
author = {Zewen, Wang and Shufang, Qiu and Yu, Shuang and Wu, Bin and Zhang, Wen},
title = {Exponential Tikhonov Regularization Method for Solving an Inverse Source Problem of Time Fractional Diffusion Equation},
journal = {Journal of Computational Mathematics},
year = {2023},
volume = {41},
number = {2},
pages = {173--190},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2107-m2020-0133},
url = {https://global-sci.com/article/84110/exponential-tikhonov-regularization-method-for-solving-an-inverse-source-problem-of-time-fractional-diffusion-equation}
}