Институт вычислительной математики и математической геофизики СОРАН

Abstracts

numerical solution of DE and IE

ANALYSIS OF PROPERTIES OF DIFFERENTIAL AND GUARANTEED BOUNDS OF SOLUTIONS AN Rogalyov Institute of Computational Modeling SB RAS Akademgorodok, Krasnoyarsk, 660036, Russia, tel. (3912) -2498329 rogalyov@icm.krasn.ru We consider a system of ordinary differential equations, whose right side depends of the actions determined by our choice, and depends of the perturbation of the system. It is required to calculate the solutions bounds, when there are known only the bounds of the initial values or boundary conditions. The general principle which integrates such a wide class of problems is, is the analysis of behavior state of the object (system) for the entire range of disturbance factors formed by extreme (most unfavorable) values of these parameters. The report describes the application of methods for estimating the safety and security boundaries of the sets of solutions to differential equations, based on a symbolic representation of the solutions and the calculation of guaranteed bounds of all solutions based on global error [1] - [7]. The results of estimating the solutions of many differential equations that appear in the problems of identifying areas of security (breach the boundaries of which leads to quite small changes in the states), the problems of estimation of reachable sets of control systems and in problems of practical stability under constantly acting perturbations in a finite time interval. 1.Novikov VA Rogalyov Building converging upper and lower bounds of solutions of systems of ordinary differential equations, Journal of Computational Mathematics and Mathematical Physics. 1993. T.33 number 2.S.219 -231. 2.Rogalyov AN Guaranteed methods for solving systems of ordinary differential equations based on the transformation of symbolic expressions / / Computational technolgies. - 2003. v. 8. № 5 - p.102-116. 3.Rogalyov AN Methods for determining the upper and lower bounds of solutions of differential equations and their applications, Proceedings of the International Conference on computational Mathematics ICCM-2004. / Edited by G.A. Mikhailov, V.P. Iljin, Yu.M. Laevskyi - Novosibirsk: ICM & MG SB RAS. - 2004, Part 2 .- S. 614-620. 4. Rogalyov A.N. Guaranteed bounds for solutions of differential equations / Tikhonov and Modern Mathematics: Computational Mathematics and Computer Science: the International Conference, Moscow Lomonosov Moscow State University. MV Lomonosov, the Russian Academy of Sciences. / Faculty MSU them. MV Lomonosov Moscow State University - Moscow: Moscow State University. MV University, 2006.-S. 100 -103. 5.Rogalyov A.N. Symbolic computation in guaranteed methods, executed on multiple processors, Vestnik NGU. Series: Information Technology. - 2006, Volume 4, no. 1 - S. 56-62. 6.Rogalyov AN Calculation of safety and security boundaries making differential equations / / Proceedings of All-Russian Conference on Computational mathematicians KVM-2007 (electronic publication) .- Novosibirsk: ICM & MG SB RAS. - 2007 .- P. 67. 7. Rogalyov AN Guaranteed estimates and the construction of attainability sets for non-linear control systems / / Bulletin of Siberian State Aerospace University - 2010 - issue 5 (31) - p.148-154.

Note. Abstracts are published in author's edition

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