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Contemporary Mathematics. Fundamental Directions, 2012, Volume 46, Pages 5–30 (Mi cmfd227)  
This article is cited in 6 scientific papers (total in 6 papers)

On a problem of the constructive theory of harmonic mappings

S. I. Bezrodnykhab, V. I. Vlasova

a Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow, Russia
b Sternberg Astronomical Institute, Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (1488 kB) Citations (6)
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Abstract: The problem of irremovable error appears in finite difference realization of the Winslow approach in the constructive theory of harmonic mappings. As an example, we consider the well-known Roache–Steinberg problem and demonstrate a new approach, which allows us to construct harmonic mappings of complicated domains effectively and with high precision. This possibility is given by the analytic-numerical method of multipoles with exponential convergence rate. It guarantees effective construction of a harmonic mapping with precision controlled by an a posteriori estimate in a uniform norm with respect to the domain.
English version:
Journal of Mathematical Sciences, 2014, Volume 201, Issue 6, Pages 705–732
DOI: https://doi.org/10.1007/s10958-014-2021-x
Bibliographic databases:
Document Type: Article
UDC: 517.57
Language: Russian
Citation: S. I. Bezrodnykh, V. I. Vlasov, “On a problem of the constructive theory of harmonic mappings”, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 2, CMFD, 46, PFUR, M., 2012, 5–30; Journal of Mathematical Sciences, 201:6 (2014), 705–732
Citation in format AMSBIB
\Bibitem{BezVla12}
\by S.~I.~Bezrodnykh, V.~I.~Vlasov
\paper On a~problem of the constructive theory of harmonic mappings
\inbook Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2011). Part~2
\serial CMFD
\yr 2012
\vol 46
\pages 5--30
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd227}
\transl
\jour Journal of Mathematical Sciences
\yr 2014
\vol 201
\issue 6
\pages 705--732
\crossref{https://doi.org/10.1007/s10958-014-2021-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919883437}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Современная математика. Фундаментальные направления
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