Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 279, Issue -, Pages 277-292Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2014.11.026
Keywords
Inverse problem; Fractional diffusion equation; Optimal error bound; Simplified Tikhonov regularization method; Convergence analysis; A posteriori parameter choice
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Funding
- NSF of China [11371181, 11171136]
- Fundamental Research Funds for the Central Universities [lzujbky-2013-k02]
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In this paper, we consider a backward problem for a time-fractional diffusion equation. Such a problem is ill-posed. The optimal error bound for the problem under a source condition is analyzed. A simplified Tikhonov regularization method is utilized to solve the problem, and its convergence rates are analyzed under an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule, respectively. Numerical examples show that the proposed regularization method is effective and stable, and both parameter choice rules work well. (C) 2014 Elsevier B.V. All rights reserved.
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