(untitled) (Journal of Computational Mathematics, 2022)
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 γ, 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 γ is less than or equal to zero, the optimal convergence rate can be achieved and it is independent of the value of γ. However, when γ is greater than zero, the optimal convergence rate depends on the value of γ 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.