Quasi-reversibility and truncation methods to solve a Cauchy problem for the modified Helmholtz equation
type: Item
instance of: scholarly article
title: Quasi-reversibility and truncation methods to solve a Cauchy problem for the modified Helmholtz equation
zbMATH Open document ID: 1185.65172
author: H. H. Qin
author: Ting Wei
published in: Mathematics and Computers in Simulation
publication date: 2009-11-16T00:00:00Z
review text: The authors consider the two regularization methods for ill-posed 2D problem named in the title and prove \(L_2\) convergence to the solution assuming apriorily boundedness in \(L_2\) of the solution or of one of its derivatives (in the marching direction of the Cauchy problem). For these results to hold, they are able to specify the regularization parameters (parameter multiplying the fourth derivative, resp.\ number of terms in the Fourier series) in dependence on the data (solution bound and measuring error). In their numerical experiments they compare the two methods and a third one, the method of lines, and conclude that the truncation method performs better.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65M30
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35R25
zbMATH DE Number: 5633810
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: quasi-reversibility method
zbMATH Keywords: truncation method
zbMATH Keywords: convergence
zbMATH Keywords: regularization methods
zbMATH Keywords: ill-posed problem
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: j.matcom.2009.07.005
OpenAlex ID: W2033914750
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DOI: 10.1016/J.MATCOM.2009.07.005
description: scientific article; zbMATH DE number 5633810