TY - JOUR
T1 - Exponential Tikhonov Regularization Method for Solving an Inverse Source Problem of Time Fractional Diffusion Equation
AU - Wang , Zewen
AU - Qiu , Shufang
AU - Yu , Shuang
AU - Wu , Bin
AU - Zhang , Wen
JO - Journal of Computational Mathematics
VL - 2
SP - 173
EP - 190
PY - 2022
DA - 2022/11
SN - 41
DO - http://doi.org/10.4208/jcm.2107-m2020-0133
UR - https://global-sci.org/intro/article_detail/jcm/21175.html
KW - Exponential regularization method, Inverse source problem, Fractional diffusion equation, Ill-posed problem, Convergence rate.
AB - <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>