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

Author:

Zhang Hongwu,Zhang Xiaoju

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.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

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