Vestnik KRAUNC. Fiziko-Matematicheskie Nauki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestnik KRAUNC. Fiz.-Mat. Nauki:
Year:
Volume:
Issue:
Page:
Find






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


Vestnik KRAUNC. Fiz.-Mat. Nauki, 2021, Volume 34, Number 1, Pages 88–104 (Mi vkam458)  

INFORMATION AND COMPUTATION TECHNOLOGIES

On approximation of definite integrals by compound quadrature formulas using derivatives

V. V. Shustov

State Research Institute of Aviation Systems

Abstract: The problem of computing a definite integral of a function for which the values of itself and the set of derivatives up to a given order at the points of the interval of integration are known is considered. Composite quadrature formulas are constructed that use the values of the function and its derivatives up to the m-th order inclusive. A representation of the remainder is obtained, expressed in terms of the derivative of the corresponding order and the number of nodal points. Examples of integration of the given functions with the study of the error and its estimation are given. A comparison is made with the known numerical methods and the Euler-Maclaurin formula, which showed increased accuracy and better convergence of the two-point integration method.

Keywords: quadrature formulas using derivatives, compound quadrature formula, remainder of integration, approximation error estimate, Euler-Maclaurin formula.

DOI: https://doi.org/10.26117/2079-6641-2021-34-1-88-104

Full text: PDF file (342 kB)
Full text: http://krasec.ru/shustov-34/
References: PDF file   HTML file

UDC: 519.644
MSC: 41A55

Citation: V. V. Shustov, “On approximation of definite integrals by compound quadrature formulas using derivatives”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 34:1 (2021), 88–104

Citation in format AMSBIB
\Bibitem{Shu21}
\by V.~V.~Shustov
\paper On approximation of definite integrals by compound quadrature formulas using derivatives
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2021
\vol 34
\issue 1
\pages 88--104
\mathnet{http://mi.mathnet.ru/vkam458}
\crossref{https://doi.org/10.26117/2079-6641-2021-34-1-88-104}


Linking options:
  • http://mi.mathnet.ru/eng/vkam458
  • http://mi.mathnet.ru/eng/vkam/v34/i1/p88

    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
  • Vestnik KRAUNC. Fiziko-Matematicheskie Nauki Vestnik KRAUNC. Fiziko-Matematicheskie Nauki
    Number of views:
    This page:30
    Full text:7
    References:1

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