caa a22 4500 605518769 CHVBK 20210128100727.0 cr unu---uuuuu 210128e20150501xx s 000 0 eng 10.1007/s10559-015-9733-x doi (NATIONALLICENCE)springer-10.1007/s10559-015-9733-x Romm Ya A. P. Chekhov State Pedagogical Institute, Taganrog, Russia aut Computer-Oriented Stability Analysis Based on Recurrent Transformation of Difference Solutions of Ordinary Differential Equations [Elektronische Daten] [Ya. Romm] Criteria for the Lyapunov stability of solutions to systems of ordinary differential equations are presented in the difference, additive, and integral forms. They contain the necessary and sufficient conditions and do not transform functions in the right-hand side of the system. In general, the criteria are intended for computer implementation, and some of them for analytical research. Based on the comparison of the integrands, the stability of some systems of nonlinear equations is analyzed without a priori solutions. The programmed criteria are given for general systems, examples and results of program and numerical experiments are presented. Springer Science+Business Media New York, 2015 Lyapunov stability analysis nationallicence approximate solution of ordinary differential equations nationallicence recurrent transformations of difference solutions nationallicence numerical modeling of stability nationallicence indications of stability of linear and nonlinear systems nationallicence computer analysis of stability nationallicence Cybernetics and Systems Analysis Springer US; http://www.springer-ny.com 51/3(2015-05-01), 416-431 1060-0396 51:3<416 2015 51 10559 https://doi.org/10.1007/s10559-015-9733-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10559-015-9733-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Romm Ya A. P. Chekhov State Pedagogical Institute, Taganrog, Russia aut NATIONALLICENCE 773 0- Cybernetics and Systems Analysis Springer US; http://www.springer-ny.com 51/3(2015-05-01), 416-431 1060-0396 51:3<416 2015 51 10559