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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 12, Pages 2088–2100 (Mi zvmmf213)  

This article is cited in 7 scientific papers (total in 7 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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:12, 2002–2013

Bibliographic databases:

UDC: 519.642

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
\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
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 12
\pages 2002--2013

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Setukha A.V., “The singular integral equation method in 3-D boundary value problems and its applications”, Numerical Analysis and Applied Mathematics (ICNAAM 2012), v. A, B, AIP Conf. Proc., 1479, ed. Simos T. Psihoyios G. Tsitouras C. Anastassi Z., Amer. Inst. Physics, 2012, 720–723  crossref  mathscinet  adsnasa  isi  scopus
    2. Lebedeva S.G., Setukha A.V., “On the Numerical Solution of a Complete Two-Dimensional Hypersingular Integral Equation by the Method of Discrete Singularities”, Differ. Equ., 49:2 (2013), 224–234  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. Zakharov E.V., Ryzhakov G.V., Setukha A.V., “Numerical Solution of 3D Problems of Electromagnetic Wave Diffraction on a System of Ideally Conducting Surfaces By the Method of Hypersingular Integral Equations”, Differ. Equ., 50:9 (2014), 1240–1251  crossref  mathscinet  zmath  isi  elib  scopus
    4. Zakharov E.V., Setukha A.V., Bezobrazova E.N., “Method of Hypersingular Integral Equations in a Three-Dimensional Problem of Diffraction of Electromagnetic Waves on a Piecewise Homogeneous Dielectric Body”, Differ. Equ., 51:9 (2015), 1197–1210  crossref  mathscinet  zmath  isi  elib  scopus
    5. Daeva S.G., Setukha A.V., “Numerical Simulation of Scattering of Acoustic Waves By Inelastic Bodies Using Hypersingular Boundary Integral Equation”, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics 2014 (Icnaam-2014), AIP Conference Proceedings, 1648, eds. Simos T., Tsitouras C., Amer Inst Physics, 2015, UNSP 390004  crossref  isi  scopus
    6. Setukha A.V., Yukhman D.A., “On the solvability of a boundary value problem for the Laplace equation on a screen with a boundary condition for a directional derivative”, Differ. Equ., 52:9 (2016), 1188–1198  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. V. Setukha, “Metod granichnykh integralnykh uravnenii s gipersingulyarnymi integralami v kraevykh zadachakh”, Materialy mezhdunarodnoi konferentsii«InternationalConference onMathematicalModellinginAppliedSciences, ICMMAS-17», Sankt-Peterburgskii politekhnicheskii universitet,2428 iyulya2017 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 160, VINITI RAN, M., 2019, 114–125  mathnet  mathscinet
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