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Fundamentalnaya i Prikladnaya Matematika, 2009, Volume 15, Issue 2, Pages 191–206 (Mi fpm1220)  
This article is cited in 1 scientific paper (total in 1 paper)

On the application of nonstationary form of the Tappert equation as an artificial boundary condition

M. Yu. Trofimov, P. S. Petrov

V. I. Il'ichev Pacific Oceanological Institute of the Far Eastern Branch of RAS
Full-text PDF (158 kB) Citations (1)
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Abstract: In this paper, a nonstationary analog of the range refraction parabolic equation is derived. A new approach to the derivation of Tappert's operator asymptotic formula with the use of noncommutative analysis is presented. The obtained nonstationary equation is proposed as an artificial boundary condition for the wave equation in underwater acoustics. This form of artificial boundary condition has low computational cost and systematically takes into account variations of sound speed. This is confirmed by various numerical experiments, including propagation of normal modes and wave fields produced by point source.
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 167, Issue 6, Pages 857–867
DOI: https://doi.org/10.1007/s10958-010-9965-2
Bibliographic databases:
UDC: 519.633.6+517.95+534.2
Language: Russian
Citation: M. Yu. Trofimov, P. S. Petrov, “On the application of nonstationary form of the Tappert equation as an artificial boundary condition”, Fundam. Prikl. Mat., 15:2 (2009), 191–206; J. Math. Sci., 167:6 (2010), 857–867
Citation in format AMSBIB
\Bibitem{TroPet09}
\by M.~Yu.~Trofimov, P.~S.~Petrov
\paper On the application of nonstationary form of the Tappert equation as an artificial boundary condition
\jour Fundam. Prikl. Mat.
\yr 2009
\vol 15
\issue 2
\pages 191--206
\mathnet{http://mi.mathnet.ru/fpm1220}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2744964}
\transl
\jour J. Math. Sci.
\yr 2010
\vol 167
\issue 6
\pages 857--867
\crossref{https://doi.org/10.1007/s10958-010-9965-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77954028865}
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  • https://www.mathnet.ru/eng/fpm/v15/i2/p191
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Фундаментальная и прикладная математика
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    References:32
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