Industrial Automatic Control Systems and Controllers Annotation << Back Program Stability Analysis of Systems of Ordinary Differential Equations Based on the Multiplicative Transformations Difference Schemes and Piecewise Polynomial Approximation Solutions S.G. Bulanov, G.A. Dzhanunts A method for stability analysis of systems of ordinary differential equations (ODE) based on the multiplicative transformations difference schemes and piecewise polynomial approximation solutions is suggested. The transformation results are stability criteria in the form of necessary and suffi cient conditions. Computer modeling of the criteria allows to determine the nature of the stability of systems of ODE in real time. In order to reduce the approximation error in the design criteria, difference values are replaced by a piecewise polynomial approximation of solutions of the ODE system. The basic design of such approach is the algorithm for representing the approximated Newton polynomial on subinterval directly with numerical coeffi cients. The polynomial coeffi cients can be recovered from its roots with the use of the parallel algorithm. At the current subinterval on difference approximations the right part ODE is interpolated, coeffi cients of the interpolation polynomial are calculated, the solution is approaching with its primitive. The process is repeated iteratively until the approximation error of the right side is minimized. Computer realization has highly accurate approximation of the solution at a low time complexity due to the relatively large size of the difference step. The results of numerical experiments, confi rming the stability of the analytical assessment of the nature of the investigated systems of ODE are presented. A comparative analysis of the results of research on the nature of the stability of the proposed criteria for different methods of determining the approximate solutions in the design criteria is performed. Keywords: computer modeling of stability; solution of ordinary differential equations; piecewise polynomial approximation. Contacts: E-mail: bulanovtgpi@mail.ru, E-mail:janunts@inbox.ru Pp. 10-20.