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Differentsial'nye Uravneniya, 2004, Volume 40, Number 9, Pages 1256–1270 (Mi de11144)  
This article is cited in 4 scientific papers (total in 4 papers)

Numerical methods

Integral equations and sound propagation in a shallow sea

I. K. Lifanova, S. L. Stavtsevb

a N.E. Zhukovsky Military Engineering Academy
b Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow
Full-text PDF (2734 kB) Citations (4)
Abstract: The boundary value problem for the Helmholtz equation for the acoustic pressure in a shallow sea can be reduced to a system of integral equations (some of which can be hypersingular). We suggest a numerical method for solving this system. In this approach to the numerical solution of the sound propagation problem in a shallow sea, the surfaces of the sea, the seabed, and the layers can have an arbitrary geometric structure.
Received: 15.03.2004
English version:
Differential Equations, 2004, Volume 40, Issue 9, Pages 1330–1344
DOI: https://doi.org/10.1007/s10625-005-0012-x
Bibliographic databases:
Document Type: Article
UDC: 519.642
Language: Russian
Citation: I. K. Lifanov, S. L. Stavtsev, “Integral equations and sound propagation in a shallow sea”, Differ. Uravn., 40:9 (2004), 1256–1270; Differ. Equ., 40:9 (2004), 1330–1344
Citation in format AMSBIB
\Bibitem{LifSta04}
\by I.~K.~Lifanov, S.~L.~Stavtsev
\paper Integral equations and sound propagation in a shallow sea
\jour Differ. Uravn.
\yr 2004
\vol 40
\issue 9
\pages 1256--1270
\mathnet{http://mi.mathnet.ru/de11144}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2199977}
\transl
\jour Differ. Equ.
\yr 2004
\vol 40
\issue 9
\pages 1330--1344
\crossref{https://doi.org/10.1007/s10625-005-0012-x}
Linking options:
  • https://www.mathnet.ru/eng/de11144
  • https://www.mathnet.ru/eng/de/v40/i9/p1256
    • This publication is cited in the following 4 articles:
    1. E. G. Khalilov, “O priblizhennom reshenii odnogo klassa slabo singulyarnykh integralnykh uravnenii”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 20:3 (2020), 310–325  mathnet  crossref
    2. Stanislav Stavtsev, Lecture Notes in Computer Science, 11958, Large-Scale Scientific Computing, 2020, 165  crossref
    3. S. L. Stavtsev, Integral Methods in Science and Engineering, Volume 2, 2017, 255  crossref
    4. V. A. Gutnikov, V. Yu. Kiryakin, I. K. Lifanov, A. V. Setukha, S. L. Stavtsev, “Numerical solution to a two-dimensional hypersingular integral equation and sound propagation in urban areas”, Comput. Math. Math. Phys., 47:12 (2007), 2002–2013  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:164
    Full-text PDF :76
    References:1
     
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