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Sibirskii Matematicheskii Zhurnal, 2003, Volume 44, Number 6, Pages 1217–1225 (Mi smj1249)  
This article is cited in 19 scientific papers (total in 19 papers)

On stability of solutions to one class of nonlinear difference systems

A. Yu. Aleksandrov, A. P. Zhabko

Saint-Petersburg State University
Full-text PDF (174 kB) Citations (19)
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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.
Received: 25.07.2002
English version:
Siberian Mathematical Journal, 2003, Volume 44, Issue 6, Pages 951–958
DOI: https://doi.org/10.1023/B:SIMJ.0000007470.46246.bd
Bibliographic databases:
UDC: 517.962.2
Language: Russian
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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\transl
\jour Siberian Math. J.
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\issue 6
\pages 951--958
\crossref{https://doi.org/10.1023/B:SIMJ.0000007470.46246.bd}
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    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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