Sibirskii Zhurnal Vychislitel'noi Matematiki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sib. Zh. Vychisl. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Sib. Zh. Vychisl. Mat., 1999, Volume 2, Number 2, Pages 171–183 (Mi sjvm333)  

This article is cited in 4 scientific papers (total in 4 papers)

On the properties of an orthonormalized singular polynomials set

V. A. Rukavishnikov, E. V. Kashuba

Computing Center, Far-Eastern Branch, Russian Academy of Sciences, Khabarovsk, Russia

Abstract: The paper introduces a concept of singular polynomials, and their orthonormalized set is constructed. The recurrence formula for three neighbouring orthonormalized singular polynomials is given and an analogue of the Rodrigues formula is found. It is established that the derivatives of polynomials from the built set have a property, close to the property of orthogonality. A differential equation and a family of relations for the derivatives of orthonormalized singular polynomials have been obtained. The results are applicable to the construction and investigation of the finite element method for mathematical physics problems with a strong singularity of solution.

Full text: PDF file (554 kB)
References: PDF file   HTML file

Bibliographic databases:
UDC: 517.587
Received: 19.11.1998
Language:

Citation: V. A. Rukavishnikov, E. V. Kashuba, “On the properties of an orthonormalized singular polynomials set”, Sib. Zh. Vychisl. Mat., 2:2 (1999), 171–183

Citation in format AMSBIB
\Bibitem{RukKas99}
\by V.~A.~Rukavishnikov, E.~V.~Kashuba
\paper On the properties of an orthonormalized singular polynomials set
\jour Sib. Zh. Vychisl. Mat.
\yr 1999
\vol 2
\issue 2
\pages 171--183
\mathnet{http://mi.mathnet.ru/sjvm333}
\zmath{https://zbmath.org/?q=an:0940.42015}


Linking options:
  • http://mi.mathnet.ru/eng/sjvm333
  • http://mi.mathnet.ru/eng/sjvm/v2/i2/p171

    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

    This publication is cited in the following articles:
    1. Bespalov A., “Orthogonal Systems of Singular Functions and Numerical Treatment of Problems with Degeneration of Data”, Adv. Comput. Math., 19:1-3 (2003), 159–182  crossref  mathscinet  zmath  isi  scopus
    2. E. V. Kashuba, V. A. Rukavishnikov, “On the $p$-version of the finite element method for the boundary value problem with singularity”, Sib. zhurn. vychisl. matem., 8:1 (2005), 31–42  mathnet  zmath
    3. Rukavishnikov V.A., “Methods of Numerical Analysis for Boundary Value Problems with Strong Singularity”, Russ. J. Numer. Anal. Math. Model, 24:6 (2009), 565–590  crossref  mathscinet  zmath  isi  elib  scopus
    4. Rukavishnikov V.A., “O kraevykh zadachakh s silnoi singulyarnostyu”, Vestnik Tikhookeanskogo gosudarstvennogo universiteta, 2011, no. 2, 033–042  mathscinet  elib
  • Sibirskii Zhurnal Vychislitel'noi Matematiki
    Number of views:
    This page:122
    Full text:55
    References:31

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