A fractional Tikhonov method for solving a Cauchy problem of Helmholtz equation. Issue 10 (27th July 2017)

• Record Type: Journal Article
• Authors: Qian, Zhi; Feng, Xiaoli
• Is Part Of: Applicable analysis. Volume 96:Issue 10(2017)
• Page Start: 1656
• Page End: 1668
• Publication Date: 2017-07-27
• Subjects: Inverse problem -- ill-posed problem -- filtering idea -- fractional Tikhonov method -- Cauchy problem for Helmholtz equation; 65N20 -- 65N21 -- 65N12; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1254776
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we study a fractional Tikhonov regularization method (FTRM) for solving a Cauchy problem of Helmholtz equation in the frequency domain. On the one hand, the FTRM retains the advantage of classical Tikhonov method. On the other hand, our method can prevent the effect of oversmoothing of classical Tikhonov method and conveniently control the amount of damping. The convergence error estimates between the exact solution and its regularization approximation are constructed. Several interesting numerical examples are provided, which validate the effectiveness of the proposed method.