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Journal of Applied Mathematics
Volume 2014, Article ID 786326, 7 pages
Research Article

Comparative Analysis of Methods for Regularizing an Initial Boundary Value Problem for the Helmholtz Equation

1Institute of Computational Mathematics and Mathematical Geophysics, Akademika Lavrentjeva, No. 6, Novosibirsk 630090, Russia
2Novosibirsk State University, Pirogova Street 2, Novosibirsk 630090, Russia
3Sobolev Institute of Mathematics, 4 Academy Koptyug Avenue, Novosibirsk 630090, Russia
4National Open Research Laboratory of Information and Space Technologies, Kazakh National Technical University after K.I. Satpaev, Seifullin Street 122/22, Almaty 050013, Kazakhstan
5Kazakh National Pedagogical University Abai, 13 Dostyk Avenue, Almaty 050010, Kazakhstan

Received 10 April 2014; Revised 16 July 2014; Accepted 22 July 2014; Published 8 September 2014

Academic Editor: D. R. Sahu

Copyright © 2014 Sergey Igorevich Kabanikhin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.