Journal of Vibration Testing and System Dynamics
Symbolic Methods for Estimating the Sets of Solutions of Ordinary Differential Equations with Perturbations on a Finite Time Interval
Journal of Vibration Testing and System Dynamics 7(1) (2023) 3137  DOI:10.5890/JVTSD.2023.03.005
A. N. Rogalev
Institute of Computational Modelling SB RAS, Krasnoyarsk, 660036, Russia
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Abstract
In many papers and reports of academician N.N. Yanenko, problem statements are presented that require computing the accuracy of numerical results, depending on perturbations.
Such problems are equivalent to problems of stability research.
The problems of motion stability over a finite time interval are of considerable interest. This is also due to the fact that most of the methods for studying stability determine stability as $t \to \infty $.
Practical stability over a finite time interval means that the solutions are uniformly bounded with respect to the set of initial values
and the totality of disturbing influences.
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