Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
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



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






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


Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 1, Pages 58–71 (Mi zvmmf9793)  

This article is cited in 5 scientific papers (total in 5 papers)

Numerical solution of the Painlevé V equation

A. A. Abramova, L. F. Yukhnob

a Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
b M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow

Abstract: A numerical method for solving the Cauchy problem for the fifth Painlevé equation is proposed. The difficulty of the problem is that the unknown function can have movable singular points of the pole type; moreover, the equation has singularities at the points where the solution vanishes or takes the value 1. The positions of all of these singularities are not a priori known and are determined in the process of solving the equation. The proposed method is based on the transition to auxiliary systems of differential equations in neighborhoods of the indicated points. The equations in these systems and their solutions have no singularities at the corresponding point and its neighborhood. Numerical results illustrating the potentials of this method are presented.

Key words: Painlevé V ordinary differential equation, pole of a solution, singularity of an equation, numerical method.

DOI: https://doi.org/10.7868/S004446691301002X

Full text: PDF file (269 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2013, 53:1, 44–56

Bibliographic databases:

UDC: 519.624.2
Received: 11.05.2012

Citation: A. A. Abramov, L. F. Yukhno, “Numerical solution of the Painlevé V equation”, Zh. Vychisl. Mat. Mat. Fiz., 53:1 (2013), 58–71; Comput. Math. Math. Phys., 53:1 (2013), 44–56

Citation in format AMSBIB
\Bibitem{AbrYuk13}
\by A.~A.~Abramov, L.~F.~Yukhno
\paper Numerical solution of the Painlev\'e~V equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2013
\vol 53
\issue 1
\pages 58--71
\mathnet{http://mi.mathnet.ru/zvmmf9793}
\crossref{https://doi.org/10.7868/S004446691301002X}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3249014}
\zmath{https://zbmath.org/?q=an:06183602}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2013CMMPh..53...44A}
\elib{https://elibrary.ru/item.asp?id=18446737}
\transl
\jour Comput. Math. Math. Phys.
\yr 2013
\vol 53
\issue 1
\pages 44--56
\crossref{https://doi.org/10.1134/S0965542513010028}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000314309400004}
\elib{https://elibrary.ru/item.asp?id=21907915}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84874513795}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf9793
  • http://mi.mathnet.ru/eng/zvmmf/v53/i1/p58

    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. Abramov, L. F. Yukhno, “Numerical solution of the Painlevé VI equation”, Comput. Math. Math. Phys., 53:2 (2013), 180–193  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. A. Abramov, L. F. Yukhno, “A method for the numerical solution of the Painlevé equations”, Comput. Math. Math. Phys., 53:5 (2013), 540–563  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. Abramov A.A. Yukhno L.F., “a Method For Calculating the Painlevé Transcendents”, Appl. Numer. Math., 93:SI (2015), 262–269  crossref  mathscinet  zmath  isi  elib  scopus
    4. Bermudez D., Fernandez C D.J., Negro J., “Solutions to the Painlevé V equation through supersymmetric quantum mechanics”, J. Phys. A-Math. Theor., 49:33 (2016), 335203  crossref  mathscinet  zmath  isi  elib  scopus
    5. Peter A. Clarkson, “Open Problems for Painlevé Equations”, SIGMA, 15 (2019), 006, 20 pp.  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:287
    Full text:103
    References:53
    First page:15

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