A wavelet method for the Cauchy problem for the Helmholtz equation
type: Item
instance of: scholarly article
title: A wavelet method for the Cauchy problem for the Helmholtz equation
zbMATH Open document ID: 1264.65181
DOI: 10.5402/2012/435468
author: F. F. Dou
author: Chuli Fu
published in: ISRN Applied Mathematics
publication date: 2013-06-11T00:00:00Z
review text: Summary: We consider a Cauchy problem for the Helmholtz equation at a fixed frequency. The problem is severely ill posed in the sense that the solution (if it exists) does not depend continuously on the data. We present a wavelet method to stabilize the problem. Some error estimates between the exact solution and its approximation are given, and numerical tests verify the efficiency and accuracy of the proposed method.
Mathematics Subject Classification ID: 65N20
Mathematics Subject Classification ID: 74J20
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 6172948
Wikidata QID: Q58690428
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2012/435468
OpenAlex ID: W2073117534
cites work: Mathematics of multidimensional seismic imaging, migration, and inversion
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cites work: Approximate solution of a Cauchy problem for the Helmholtz equation
cites work: The detection of the source of acoustical noise in two dimensions
cites work: The detection of surface vibrations from interior acoustical pressure
cites work: A meshless method for some inverse problems associated with the Helmholtz equation
cites work: Relaxation of Alternating Iterative Algorithms for the Cauchy Problem Associated with the Modified Helmholtz Equation
cites work: An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation
cites work: The method of fundamental solutions for inverse boundary value problems associated with the two-dimensional biharmonic equation
cites work: A meshless method for the stable solution of singular inverse problems for two-dimensional Helmholtz-type equations
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cites work: Q3135829
cites work: Optimality for ill-posed problems under general source conditions
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description: scientific article; zbMATH DE number 6172948