Matematicheskoe modelirovanie
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Matem. Mod.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Matem. Mod., 2013, Volume 25, Number 4, Pages 65–73 (Mi mm3352)  

Computing experiments in the problem on eigenvalues for the operator of Laplace in the polygonal domain

S. D. Algazin

Establishment of the Russian Academy of Sciences Ishlinsky Institute of Problems of the Mechanics the Russian Academy of Sciences

Abstract: The technique of a numerical evaluation of eigenvalues of an operator of Laplace in a polygon is described. As an example it is considered $L$-figurative area. The circle conformal mapping on this area by means of an integral of Christoffel–Schwarz is under construction. In a circle the problem dares on earlier developed by the author (together with K. I. Babenko) a technique without saturation. The problem consists in, whether this technique to piecewise smooth boundaries (the conformal mapping has on singularity boundary) is applicable. The done evaluations show that it is possible to calculate about 5 eigenvalues (for a problem of Neumann about 100 eigenvalues) an operator of Laplace in this area with two-five signs after a comma.

Keywords: eingenvalues of an operator of Laplace, an integral of Christoffer–Schwarz, numerical algorithm without saturation.

Full text: PDF file (395 kB)
References: PDF file   HTML file

English version:
Mathematical Models and Computer Simulations, 2013, 5:6, 520–526

Bibliographic databases:

UDC: 519.632.4
Received: 17.02.2012

Citation: S. D. Algazin, “Computing experiments in the problem on eigenvalues for the operator of Laplace in the polygonal domain”, Matem. Mod., 25:4 (2013), 65–73; Math. Models Comput. Simul., 5:6 (2013), 520–526

Citation in format AMSBIB
\Bibitem{Alg13}
\by S.~D.~Algazin
\paper Computing experiments in the problem on eigenvalues for the operator of Laplace in the polygonal domain
\jour Matem. Mod.
\yr 2013
\vol 25
\issue 4
\pages 65--73
\mathnet{http://mi.mathnet.ru/mm3352}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3114885}
\transl
\jour Math. Models Comput. Simul.
\yr 2013
\vol 5
\issue 6
\pages 520--526
\crossref{https://doi.org/10.1134/S2070048213060021}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84929087608}


Linking options:
  • http://mi.mathnet.ru/eng/mm3352
  • http://mi.mathnet.ru/eng/mm/v25/i4/p65

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математическое моделирование
    Number of views:
    This page:289
    Full text:78
    References:25
    First page:20

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021