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Stationary iterated weighted Tikhonov regularization method for identifying an unknown source term of time-fractional radial heat equation

Abstract

The ill-posed problem of unknown source identification in the time-fractional radial heat conduction equation is studied. In order to overcome the ill-posedness of the problem, a stationary iterated weighted Tikhonov regularization method is proposed. The a-priori and the a-posteriori choice rules for regularization parameters are discussed and the corresponding convergence rates of both are obtained. The stationary iterated weighted Tikhonov regularization method goes beyond the saturation results of weighted Tikhonov regularization method. A numerical example shows the effectiveness of this method.

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Acknowledgements

We thank the referees for careful reviewing and for pointing out some nice ideas. This work is supported by the foundation of Shaanxi University of Technology (SLGRCQD2023), the Scientific Research Program Foundation of Shaanxi Provincial Education Department (No. 18JK0166).

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Correspondence to Xiangtuan Xiong.

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Yang, S., Xiong, X., Pan, P. et al. Stationary iterated weighted Tikhonov regularization method for identifying an unknown source term of time-fractional radial heat equation. Numer Algor (2021). https://doi.org/10.1007/s11075-021-01213-7

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Keywords

  • Inverse source problem
  • Stationary iterated weighted Tikhonov
  • Error estimate

Mathematics Subject Classification (2010)

  • 35R25
  • 35R30
  • 65J20
  • 65M30