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

Hongwu Zhang and Xiaoju Zhang
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Hongwu Zhang: School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
Xiaoju Zhang: Center for Faculty Development, North Minzu University, Yinchuan 750021, China

Mathematics, 2020, vol. 8, issue 1, 1-19

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.

Keywords: Cauchy problem; elliptic equation; regularization method; a-priori and a-posteriori convergence estimates; numerical simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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