RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sib. Èlektron. Mat. Izv.:
Year:
Volume:
Issue:
Page:
Find






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


Sib. Èlektron. Mat. Izv., 2011, Volume 8, Pages 273–283 (Mi semr323)  

This article is cited in 8 scientific papers (total in 8 papers)

On calculation of Chebyshev series coefficients for the solutions to ordinary differential equations

O. B. Arushanyan, N. I. Volchenskova, S. F. Zaletkin

Research Computer Center, M. V. Lomonosov Moscow State University

Abstract: Canonical systems of second-order ordinary differential equations are considered. The solution of such a system and its derivatives are expanded in shifted series in Chebyshev polynomials of the first kind. Algorithms to determine initial approximations for the expansion coefficients are described. The resulting approximations are used in the method of approximate analytical integration of ordinary differential equations on the basis of Chebyshev series.

Keywords: ordinary differential equations, numerical methods.

Full text: PDF file (763 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 519.62
MSC: 65L05
Received April 26, 2011, published September 14, 2011

Citation: O. B. Arushanyan, N. I. Volchenskova, S. F. Zaletkin, “On calculation of Chebyshev series coefficients for the solutions to ordinary differential equations”, Sib. Èlektron. Mat. Izv., 8 (2011), 273–283

Citation in format AMSBIB
\Bibitem{AruVolZal11}
\by O.~B.~Arushanyan, N.~I.~Volchenskova, S.~F.~Zaletkin
\paper On calculation of Chebyshev series coefficients for the solutions to ordinary differential equations
\jour Sib. \`Elektron. Mat. Izv.
\yr 2011
\vol 8
\pages 273--283
\mathnet{http://mi.mathnet.ru/semr323}


Linking options:
  • http://mi.mathnet.ru/eng/semr323
  • http://mi.mathnet.ru/eng/semr/v8/p273

    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. A. A. Gonchar, E. A. Rakhmanov, S. P. Suetin, “Padé–Chebyshev approximants of multivalued analytic functions, variation of equilibrium energy, and the $S$-property of stationary compact sets”, Russian Math. Surveys, 66:6 (2011), 1015–1048  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. O. B. Arushanyan, N. I. Volchenskova, S. F. Zaletkin, “Primenenie ryadov Chebysheva dlya integrirovaniya obyknovennykh differentsialnykh uravnenii”, Sib. elektron. matem. izv., 11 (2014), 517–531  mathnet
    3. I. I. Sharapudinov, “Some special series in ultraspherical polynomials and their approximation properties”, Izv. Math., 78:5 (2014), 1036–1059  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. I. I. Sharapudinov, “Nekotorye spetsialnye dvumernye ryady po sisteme $\{\sin x\sin kx\}$ i ikh approksimativnye svoistva”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4(1) (2014), 407–412  mathnet
    5. I. I. Sharapudinov, G. G. Akniev, “Diskretnye preobrazovaniya so svoistvom prilipaniya na osnove sistemy $\{\sin x\sin kx\}$ i sistemy polinomov Chebysheva vtorogo roda”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4(1) (2014), 413–422  mathnet
    6. O. B. Arushanyan, N. I. Volchenskova, S. F. Zaletkin, “On an approach to integration of ordinary differential equations with the use of series”, Moscow University Mathematics Bulletin, 69:6 (2014), 272–274  mathnet  crossref  mathscinet
    7. I. I. Sharapudinov, T. I. Sharapudinov, “Ob odnovremennom priblizhenii funktsii i ikh proizvodnykh posredstvom polinomov Chebysheva, ortogonalnykh na ravnomernoi setke”, Dagestanskie elektronnye matematicheskie izvestiya, 2015, no. 4, 74–117  mathnet  crossref  elib
    8. O. B. Arushanyan, N. I. Volchenskova, S. F. Zaletkin, “Application of Chebyshev series to integration of ordinary differential equations with rapidly growing solutions”, Moscow University Mathematics Bulletin, 70:5 (2015), 237–240  mathnet  crossref  mathscinet
  • Number of views:
    This page:262
    Full text:76
    References:18

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019