Name
Title | ||
|---|---|---|
A Tikhonov regularization method for solving a backward time–space fractional diffusion problem |
Abstract | ||
|---|---|---|
In this paper, a backward problem for a time–space fractional diffusion equation is considered, which is to determine the initial data from a noisy final data. To deal with this ill-posed problem, combined the ideas of the Tikhonov regularization in Hilbert Schales proposed by Natterer in 1984 and the fractional Tikhonov method given by Hochstenbach–Reichel in 2011, a Tikhonov regularization method is constructed. Based on the Fourier transform, an a-priori and an a-posteriori regularization parameter choice rules are used to guarantee the order optimal convergence rates. By the finite difference methods and the Discrete Fourier transform, numerical examples in one-dimensional and two-dimensional cases are given for the a-posteriori regularization parameter choice rule. Theoretical and numerical results show that the proposed method works well for both the smooth and the non-smooth functions. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1016/j.cam.2022.114236 | Journal of Computational and Applied Mathematics |
Keywords | DocType | Volume |
35R25,47A52,35R30 | Journal | 411 |
ISSN | Citations | PageRank |
0377-0427 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xiaoli Feng | 1 | 0 | 0.34 |
| Meixia Zhao | 2 | 0 | 0.34 |
| Zhi Qian | 3 | 41 | 7.81 |