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Sib. Zh. Ind. Mat., 2016, Volume 19, Number 2, Pages 47–60 (Mi sjim920)  

This article is cited in 1 scientific paper (total in 1 paper)

On a class of systems of ordinary differential equations of large dimension

G. V. Demidenkoab, I. A. Uvarovaa

a Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk
b Novosibirsk State University, 2 Pirogova str., 630090 Novosibirsk

Abstract: We consider the Cauchy problem for a class of systems of ordinary differential equations of large dimension. We prove that, for a sufficiently many equations, the last component of the solution to the Cauchy problem is an approximate solution to an initial value problem for a delay differential equation. Estimates of the approximation are obtained.

Keywords: system of ordinary differential equations of large dimension, limit theorem, delay differential equation.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-31528


DOI: https://doi.org/10.17377/sibjim.2016.19.205

Full text: PDF file (250 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2016, 10:2, 179–191

Bibliographic databases:

UDC: 517.925.5+517.929
Received: 17.08.2015

Citation: G. V. Demidenko, I. A. Uvarova, “On a class of systems of ordinary differential equations of large dimension”, Sib. Zh. Ind. Mat., 19:2 (2016), 47–60; J. Appl. Industr. Math., 10:2 (2016), 179–191

Citation in format AMSBIB
\Bibitem{DemUva16}
\by G.~V.~Demidenko, I.~A.~Uvarova
\paper On a~class of systems of ordinary differential equations of large dimension
\jour Sib. Zh. Ind. Mat.
\yr 2016
\vol 19
\issue 2
\pages 47--60
\mathnet{http://mi.mathnet.ru/sjim920}
\crossref{https://doi.org/10.17377/sibjim.2016.19.205}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3549866}
\elib{http://elibrary.ru/item.asp?id=26001726}
\transl
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
\issue 2
\pages 179--191
\crossref{https://doi.org/10.1134/S1990478916020034}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84971264840}


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    This publication is cited in the following articles:
    1. G. V. Demidenko, I. A. Uvarova, Yu. A. Khazova, “On one system of ordinary differential equations of large dimension and a delay equation”, J. Appl. Industr. Math., 13:3 (2019), 447–459  mathnet  crossref  crossref  elib
  • Сибирский журнал индустриальной математики
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