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A quasi-reversibility method for solving a two-dimensional time-fractional inverse heat conduction problem

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  • Wang, Yan
  • Qian, Zhi

Abstract

In this paper, we consider a two-dimensional time-fractional inverse heat conduction problem, which is severely ill-posed. A quasi-reversibility method is proposed to solve this problem with disturbed boundary value. We give the selection of regularization parameters of quasi-reversibility method both under a priori and a posteriori rules, and give the proof of error estimates between the exact solution and its regularization approximation. Further more, numerical results are included to verify the effectiveness of the proposed method.

Suggested Citation

  • Wang, Yan & Qian, Zhi, 2023. "A quasi-reversibility method for solving a two-dimensional time-fractional inverse heat conduction problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 423-440.
    • Handle: RePEc:eee:matcom:v:212:y:2023:i:c:p:423-440
    DOI: 10.1016/j.matcom.2023.05.012
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    References listed on IDEAS

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    1. Zheng, G.H. & Wei, T., 2010. "Spectral regularization method for the time fractional inverse advection–dispersion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 37-51.
    2. Yang, Fan & Fu, Chu-Li & Li, Xiao-Xiao, 2018. "The method of simplified Tikhonov regularization for a time-fractional inverse diffusion problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 219-234.
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