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Sibirskii Matematicheskii Zhurnal, 2021, Volume 62, Number 4, Pages 784–802
DOI: https://doi.org/10.33048/smzh.2021.62.407 (Mi smj7595) 		 
This article is cited in 1 scientific paper (total in 1 paper)

A one-parametric method for determining parameters in the Schwarz–Christoffel integral

I. A. Kolesnikov

Tomsk State University, Tomsk, Russia
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DOI: https://doi.org/10.33048/smzh.2021.62.407
Abstract: We propose a method for determining parameters in the Schwarz–Christoffel integral. The desired mapping embeds into a one-parametric family of conformal mappings of the upper half-plane onto the family of polygons which was obtained by shifting one or several vertices of some initial polygon with angle preservation. We consider the case when the family of polygons and the initial polygon have the same number of vertices; the case when the family of polygons has two mobile vertices coinciding at the initial moment and not coinciding with other vertices; and the other case that the family of polygons is a polygon with mobile cut. The problem of finding the parameters of a family of mappings is reduced to integrating some system of ordinary differential equations.
Keywords: conformal mapping, polygon, Schwarz–Christoffel integral.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation
The author was supported by the Ministry of Science and Higher Education of the Russian Federation (the project of the Regional Scientific-Educational Mathematical Center of Tomsk State University).
Received: 30.12.2020
Revised: 25.05.2021
Accepted: 11.06.2021
English version:
Siberian Mathematical Journal, 2021, Volume 62, Issue 4, Pages 638–653
DOI: https://doi.org/10.1134/S0037446621040078
Bibliographic databases:
Document Type: Article
UDC: 517.542
Language: Russian
Citation: I. A. Kolesnikov, “A one-parametric method for determining parameters in the Schwarz–Christoffel integral”, Sibirsk. Mat. Zh., 62:4 (2021), 784–802; Siberian Math. J., 62:4 (2021), 638–653
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/smj/v62/i4/p784
    • This publication is cited in the following articles:
    1. I. A. Kolesnikov, “Konformnoe otobrazhenie poluploskosti na schetnougolnik tipa poluploskosti”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2022, no. 77, 5–16  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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