Abstract
In this article, we consider an inverse problem of recovering the potential term in a 1D time-fractional diffusion equation from the overdetermined final time data. We introduce a reconstruction operator and show its contractivity and monotonicity, which give the unique determination and an efficient algorithm. Further, for noisy data, we propose a regularized iterative algorithm based on mollification and derive error estimates for the approximation. Extensive numerical experiments for both smooth and nonsmooth potential data are provided to illustrate the efficiency and stability of the algorithm, and to verify the convergence theory.
Original language | English |
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Pages (from-to) | 579-600 |
Number of pages | 22 |
Journal | IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) |
Volume | 82 |
Issue number | 3 |
DOIs | |
Publication status | Published - 27 Feb 2017 |
Externally published | Yes |
Keywords
- Contraction
- Fractional diffusion
- Inverse potential problem
- Iterative algorithm
- Monotonicity
- Regularization
ASJC Scopus subject areas
- Applied Mathematics