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Contemporary Mathematics. Fundamental Directions, 2010, Volume 36, Pages 36–49 (Mi cmfd154)  
This article is cited in 22 scientific papers (total in 22 papers)

Boundary-value problems for the Helmholtz equation and their discrete mathematical models

Yu. V. Gandel'

V. N. Karazin Kharkiv National University, Khar'kov, Ukraine
Full-text PDF (181 kB) Citations (22)
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Abstract: We consider boundary-value problems of mathematical diffraction theory and discuss the possibility of reducing them to boundary hypersingular integral equations and solving them numerically. The analytic technique of parametric representations of pseudodifferential and integral operators and the numerical method of discrete singularities are essentially used. We discuss the reasoning in applying this approach to constructing mathematical models of wave diffraction problems and solving them numerically.
English version:
Journal of Mathematical Sciences, 2010, Volume 171, Issue 1, Pages 74–88
DOI: https://doi.org/10.1007/s10958-010-0127-3
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. V. Gandel', “Boundary-value problems for the Helmholtz equation and their discrete mathematical models”, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 2, CMFD, 36, PFUR, M., 2010, 36–49; Journal of Mathematical Sciences, 171:1 (2010), 74–88
Citation in format AMSBIB
\Bibitem{Gan10}
\by Yu.~V.~Gandel'
\paper Boundary-value problems for the Helmholtz equation and their discrete mathematical models
\inbook Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17--24, 2008). Part~2
\serial CMFD
\yr 2010
\vol 36
\pages 36--49
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd154}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2752648}
\transl
\jour Journal of Mathematical Sciences
\yr 2010
\vol 171
\issue 1
\pages 74--88
\crossref{https://doi.org/10.1007/s10958-010-0127-3}
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    • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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