Comparative Analysis of Methods for Regularizing an Initial Boundary Value Problem for the Helmholtz Equation. (7th September 2014)

• Record Type: Journal Article
• Authors: Kabanikhin, Sergey Igorevich; Shishlenin, M. A.; Nurseitov, D. B.; Nurseitova, A. T.; Kasenov, S. E.
• Other Names: Sahu D. R. Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2014(2014)
• Publication Date: 2014-09-07
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2014/786326
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : We consider an ill-posed initial boundary value problem for the Helmholtz equation. This problem is reduced to the inverse continuation problem for the Helmholtz equation. We prove the well-posedness of the direct problem and obtain a stability estimate of its solution. We solve numerically the inverse problem using the Tikhonov regularization, Godunov approach, and the Landweber iteration. Comparative analysis of these methods is presented.