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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 12, Pages 2088–2100 (Mi zvmmf213)  
This article is cited in 8 scientific papers (total in 8 papers)

Numerical solution to a two-dimensional hypersingular integral equation and sound propagation in urban areas

V. A. Gutnikova, V. Yu. Kiryakinb, I. K. Lifanovc, A. V. Setukhac, S. L. Stavtsevd

a Faculty of Ecology, Peoples' Friendship University of Russia, Podol'skoe sh. 8/5, Moscow, 113093, Russia
b All-Russia Research Institute of Railroad Transportation, Federal Agency for Rail Transportation, Tret'ya Mytishchinskaya ul. 10, Moscow, 129626, Russia
c Department of Mathematics, Zhukovsky Air Force Engineering Academy, ul. Planetnaya 3, Moscow, 125190, Russia
d Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia
Full-text PDF (2249 kB) Citations (8)
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Abstract: A mathematical model of sound propagation from a noise source in urban areas is constructed. The exterior Neumann problem for the scalar Helmholtz equation is reduced to a system of hypersingular integral equations. A numerical method for solving the system of integral equations is described. The convergence of the quadrature formulas underlying the numerical method is estimated. Numerical results are presented for particular applications.
Key words: acoustics problems, hypersingular integral equations, closed discrete vortical frames method, estimates for quadrature formulas.
English version:
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Issue 12, Pages 2002–2013
DOI: https://doi.org/10.1134/S096554250712010X
Bibliographic databases:
Document Type: Article
UDC: 519.642
Language: Russian
Citation: 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”, Zh. Vychisl. Mat. Mat. Fiz., 47:12 (2007), 2088–2100; Comput. Math. Math. Phys., 47:12 (2007), 2002–2013
Citation in format AMSBIB
\Bibitem{GutKirLif07}
\by V.~A.~Gutnikov, V.~Yu.~Kiryakin, I.~K.~Lifanov, A.~V.~Setukha, S.~L.~Stavtsev
\paper Numerical solution to a~two-dimensional hypersingular integral equation and sound propagation in urban areas
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 12
\pages 2088--2100
\mathnet{http://mi.mathnet.ru/zvmmf213}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2394966}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 12
\pages 2002--2013
\crossref{https://doi.org/10.1134/S096554250712010X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-37649017520}
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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