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Sibirsk. Mat. Zh., 2003, Volume 44, Number 6, Pages 1217–1225 (Mi smj1249)  

This article is cited in 7 scientific papers (total in 7 papers)

On stability of solutions to one class of nonlinear difference systems

A. Yu. Aleksandrov, A. P. Zhabko

Saint-Petersburg State University

Abstract: We consider some class of systems of nonlinear ordinary differential equations. We adjust the difference schemes corresponding to the equations under study in order to guarantee agreement between differential and difference systems in the sense of stability of the zero solution. We obtain conditions under which perturbations do not violate the asymptotic stability of solutions to difference systems.

Keywords: stability of difference systems, Lyapunov function, conservative numerical methods, stability in nonlinear approximation

Full text: PDF file (174 kB)
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English version:
Siberian Mathematical Journal, 2003, 44:6, 951–958

Bibliographic databases:

UDC: 517.962.2
Received: 25.07.2002

Citation: A. Yu. Aleksandrov, A. P. Zhabko, “On stability of solutions to one class of nonlinear difference systems”, Sibirsk. Mat. Zh., 44:6 (2003), 1217–1225; Siberian Math. J., 44:6 (2003), 951–958

Citation in format AMSBIB
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\paper On stability of solutions to one class of nonlinear difference systems
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 6
\pages 1217--1225
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2034929}
\zmath{https://zbmath.org/?q=an:1044.34010}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 6
\pages 951--958
\crossref{https://doi.org/10.1023/B:SIMJ.0000007470.46246.bd}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000187464000002}


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    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. Ya. E. Romm, “Modelirovanie ustoichivosti po Lyapunovu na osnove preobrazovanii raznostnykh reshenii obyknovennykh differentsialnykh uravnenii”, Matem. modelirovanie, 20:12 (2008), 105–118  mathnet  mathscinet  zmath
    2. A. Yu. Aleksandrov, A. P. Zhabko, “Preservation of stability under discretization of systems of ordinary differential equations”, Siberian Math. J., 51:3 (2010), 383–395  mathnet  crossref  mathscinet  zmath  isi
    3. A. Yu. Aleksandrov, A. V. Platonov, “On stability of solutions for a class of nonlinear difference systems with switching”, Autom. Remote Control, 77:5 (2016), 779–788  mathnet  crossref  isi  elib  elib
    4. Zeng Ch., Xiang Sh., Liang Sh., “Asymptotic Behaviours and Stability of Zero Dynamics in Nonlinear Discrete-Time Systems Using Taylor Approach and Multirate Input”, Int. J. Syst. Sci., 48:7 (2017), 1556–1568  crossref  mathscinet  zmath  isi  scopus
    5. V. V. Provotorov, E. N. Provotorova, “Sintez optimalnogo granichnogo upravleniya parabolicheskoi sistemy s zapazdyvaniem i raspredelennymi parametrami na grafe”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 13:2 (2017), 209–224  mathnet  crossref  elib
    6. V. V. Provotorov, V. I. Ryazhskikh, Yu. A. Gnilitskaya, “Unique weak solvability of a nonlinear initial boundary value problem with distributed parameters in a netlike domain”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 13:3 (2017), 264–277  mathnet  crossref  elib
    7. A. P. Zhabko, V. V. Provotorov, O. R. Balaban, “Stabilization of weak solutions of parabolic systems with distributed parameters on the graph”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 15:2 (2019), 187–198  mathnet  crossref  elib
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