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Generalized-Fractional Tikhonov-Type Method for the Cauchy Problem of Elliptic Equation

Author

Listed:
  • Hongwu Zhang

    (School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
    These authors contributed equally to this work.)

  • Xiaoju Zhang

    (Center for Faculty Development, North Minzu University, Yinchuan 750021, China
    These authors contributed equally to this work.)

Abstract

This article researches an ill-posed Cauchy problem of the elliptic-type equation. By placing the a-priori restriction on the exact solution we establish conditional stability. Then, based on the generalized Tikhonov and fractional Tikhonov methods, we construct a generalized-fractional Tikhonov-type regularized solution to recover the stability of the considered problem, and some sharp-type estimates of convergence for the regularized method are derived under the a-priori and a-posteriori selection rules for the regularized parameter. Finally, we verify that the proposed method is efficient and acceptable by making the corresponding numerical experiments.

Suggested Citation

  • Hongwu Zhang & Xiaoju Zhang, 2020. "Generalized-Fractional Tikhonov-Type Method for the Cauchy Problem of Elliptic Equation," Mathematics, MDPI, vol. 8(1), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:48-:d:304193
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