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Regularization methods for unknown source in space fractional diffusion equation

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  • Tian, WenYi
  • Li, Can
  • Deng, Weihua
  • Wu, Yujiang

Abstract

We discuss determining the unknown steady source in a space fractional diffusion equation and show that both the Fourier and wavelet dual least squares regularization methods work well for the ill-posed problem. The detailed error estimates are also strictly established for both of the methods. Moreover, the algorithm implementation and the corresponding numerical results are presented for the Fourier regularization method.

Suggested Citation

  • Tian, WenYi & Li, Can & Deng, Weihua & Wu, Yujiang, 2012. "Regularization methods for unknown source in space fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 45-56.
    • Handle: RePEc:eee:matcom:v:85:y:2012:i:c:p:45-56
    DOI: 10.1016/j.matcom.2012.08.011
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    1. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
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    Cited by:

    1. Zheng, Guang-Hui & Zhang, Quan-Guo, 2018. "Solving the backward problem for space-fractional diffusion equation by a fractional Tikhonov regularization method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 148(C), pages 37-47.
    2. Yu, Bo & Jiang, Xiaoyun & Wang, Chu, 2016. "Numerical algorithms to estimate relaxation parameters and Caputo fractional derivative for a fractional thermal wave model in spherical composite medium," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 106-118.

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