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Iteration regularization method for a sideways problem of time-fractional diffusion equation

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Abstract

We investigate a sideways problem of the time-fractional diffusion equation. This problem is ill-posed in the sense that the solution (if it exists) does not depend on the measured data. This article constructs an iteration regularization method to overcome the ill-posedness of considered problem. Under the a priori and a posteriori selection rules for the regularized parameter, the convergence results of optimal order for the proposed method are derived. We also verify the simulation effectiveness of our method by doing the corresponding numerical experiments. Numerical results show that this method is stable and feasible in solving the sideways problem of time-fractional diffusion equation.

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Acknowledgements

The authors would like to thank the reviewers for their constructive comments and valuable suggestions that improve the quality of our paper. The work described in this paper was supported by the NSF of China (11761004) and the Construction Project of First-Class Disciplines in Ningxia Higher Education (NXYLXK2017B09).

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  1. School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, Ningxia, China

    Hongwu Zhang & Yong Lv

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  1. Hongwu Zhang
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Correspondence to Hongwu Zhang.

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Zhang, H., Lv, Y. Iteration regularization method for a sideways problem of time-fractional diffusion equation. Numer Algor 91, 1145–1163 (2022). https://doi.org/10.1007/s11075-022-01295-x

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