Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Guidelines for authors

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zhurnal SVMO:
Year:
Volume:
Issue:
Page:
Find






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


Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva, 2021, Volume 23, Number 4, Pages 360–378
DOI: https://doi.org/10.15507/2079-6900.23.202104.360-378
(Mi svmo806)
 

Mathematics

Optimal with respect to accuracy methods for evaluating hypersingular integrals

I. V. Boykov, A. I. Boikova

Penza State University
References:
Abstract: In this paper we constructed optimal with respect to order quadrature formulas for evaluating one- and multidimensional hypersingular integrals on classes of functions $\Omega_{r,\gamma}^{u}(\Omega,M),$ $\bar \Omega_{r,\gamma}^{u}(\Omega,M)$, $\Omega=[-1,1]^l,$ $l=1,2,\ldots,M=Const,$ and $\gamma$ is a real positive number. The functions that belong to classes $\Omega_{r,\gamma}^{u}(\Omega,M)$ and $\bar \Omega_{r,\gamma}^{u}(\Omega,M)$ have bounded derivatives up to the $r$th order in domain $\Omega$ and derivatives up to the $s$th order $(s=r+\lceil \gamma \rceil)$ in domain $\Omega \backslash \Gamma,$ $\Gamma = \partial \Omega.$ Moduli of derivatives of the $v$th order $(r < v \le s)$ are power functions of $d(x,\Gamma)^{-1}(1+|\ln d(x,\Gamma)|),$ where $d(x,\Gamma)$ is a distance between point $x$ and $\Gamma.$ The interest in these classes of functions is due to the fact that solutions of singular and hypersingular integral equations are their members. Moreover various physical fields, in particular gravitational and electromagnetic fields belong to these classes as well. We give definitions of optimal with respect to accuracy methods for solving hypersingular integrals. We constructed optimal with respect to order of accuracy quadrature formulas for evaluating one- and multidimensional hypersingular integrals on classes of functions $\Omega_{r,\gamma}^{u}(\Omega,M)$ and $\bar \Omega_{r,\gamma}^{u}(\Omega,M)$.
Keywords: hypersingular integrals, quadrature formulas, optimal methods.
Document Type: Article
UDC: 517.392
MSC: 65D32
Language: Russian
Citation: I. V. Boykov, A. I. Boikova, “Optimal with respect to accuracy methods for evaluating hypersingular integrals”, Zhurnal SVMO, 23:4 (2021), 360–378
Citation in format AMSBIB
\Bibitem{BoyBoi21}
\by I.~V.~Boykov, A.~I.~Boikova
\paper Optimal with respect to accuracy methods for evaluating hypersingular integrals
\jour Zhurnal SVMO
\yr 2021
\vol 23
\issue 4
\pages 360--378
\mathnet{http://mi.mathnet.ru/svmo806}
\crossref{https://doi.org/10.15507/2079-6900.23.202104.360-378}
Linking options:
  • https://www.mathnet.ru/eng/svmo806
  • https://www.mathnet.ru/eng/svmo/v23/i4/p360
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024