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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


IMPACT FACTOR 2017: 0.941
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CiteScore 2017: 0.91

SCImago Journal Rank (SJR) 2017: 0.461
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Online
ISSN
1569-3945
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Volume 22, Issue 2

Issues

A comparison of regularization methods for identifying unknown source problem for the modified Helmholtz equation

Jingjun Zhao / Songshu Liu / Tao Liu
Published Online: 2013-11-23 | DOI: https://doi.org/10.1515/jip-2012-0059

Abstract.

In this paper, three regularization methods, such as the mollification method, the modified Tikhonov regularization method, the Fourier regularization method, for the identification of an unknown source for the modified Helmholtz equation are considered and compared. We have solved the model problem with these methods, investigated the differences between them, analyzed their convergence estimates under a priori choice of the regularization parameter and proved the effectiveness of these methods. Two numerical examples are provided to show the main results.

Keywords: Ill-posed problem; regularization methods; unknown source; modified Helmholtz equation

MSC: 47A52; 65J22

About the article

Received: 2012-03-29

Published Online: 2013-11-23

Published in Print: 2014-04-01


Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11101109

Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11271102

Funding Source: Natural Science Foundation of Hei-long-jiang Province of China

Award identifier / Grant number: A201107


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 22, Issue 2, Pages 277–296, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jip-2012-0059.

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