The truncation method for the Cauchy problem of the inhomogeneous Helmholtz equation. Issue 5 (4th April 2019)

• Record Type: Journal Article
• Authors: Yang, Fan; Zhang, Pan; Li, Xiao-Xiao
• Is Part Of: Applicable analysis. Volume 98:Issue 5(2019)
• Page Start: 991
• Page End: 1004
• Publication Date: 2019-04-04
• Subjects: Inhomogeneous Helmholtz equation -- ill-posed problem -- regularization method -- error estimate; 35R25 -- 47A52 -- 35R30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1408080
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, the Cauchy problem of inhomogeneous Helmholtz equation is investigated. This problem is ill-posed and the truncation method is used to solve this inverse problem. Under the a priori and a posteriori parameter choice rules, the error estimates between the regularization solution and the exact solution is obtained, respectively. Numerical examples show that the truncation method works effectively.