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Regularization methods for solving a time-fractional diffusion inverse source problem

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  • Wu, Hanghang
  • Yang, Hongqi

Abstract

This paper studies a time-fractional diffusion ill-posed inverse source problem. We use a simplified Tikhonov regularization method and a Fourier regularization method to solve the problem. Under the selection rules of a priori and a posteriori regularization parameters, a priori and a posteriori error estimates are derived. Among them, the a priori error estimate derived from the simplified Tikhonov regularization method is optimal, while the a posteriori error estimate is quasi-optimal. The a priori and a posteriori error estimates derived by the Fourier regularization method are both optimal. Finally, numerical examples are conducted to demonstrate the effectiveness and stability of the proposed regularization methods.

Suggested Citation

  • Wu, Hanghang & Yang, Hongqi, 2025. "Regularization methods for solving a time-fractional diffusion inverse source problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 232(C), pages 295-310.
    • Handle: RePEc:eee:matcom:v:232:y:2025:i:c:p:295-310
    DOI: 10.1016/j.matcom.2025.01.002
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    1. Huang, Chaobao & Yu, Xijun & Wang, Cheng & Li, Zhenzhen & An, Na, 2015. "A numerical method based on fully discrete direct discontinuous Galerkin method for the time fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 483-492.
    2. Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
    3. Zhi-Liang Deng & Xiao-Mei Yang & Xiao-Li Feng, 2013. "A Mollification Regularization Method for a Fractional-Diffusion Inverse Heat Conduction Problem," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-9, February.
    4. Deng, Zhi-Liang & Fu, Chu-Li & Feng, Xiao-Li & Zhang, Yuan-Xiang, 2011. "A mollification regularization method for stable analytic continuation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1593-1608.
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