Solving the backward problem for space-fractional diffusion equation by a fractional Tikhonov regularization method

Guang-Hui Zheng and Quan-Guo Zhang

Mathematics and Computers in Simulation (MATCOM), 2018, vol. 148, issue C, 37-47

Abstract: In this paper, we consider the backward problem for diffusion equation with space-fractional Laplacian. In order to overcome the ill-posedness of the backward problem, we propose a fractional Tikhonov regularization method to solve it. Based on the conditional stability estimate and an a posteriori regularization parameter choice rule, the convergence rate estimate is presented under a-priori bound assumption for the exact solution. Finally, several numerical examples are given to show that the proposed numerical methods are effective.

Keywords: Backward problem; Fractional Tikhonov regularization method; Fractional Laplacian; Convergence rate estimate; a posteriori parameter choice (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:148:y:2018:i:c:p:37-47

DOI: 10.1016/j.matcom.2017.12.005

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