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Article information
1999 , Volume 4, ¹ 4, p.51-75
Rogalev A.N., Shokin Y.I.
Examining and estimating solutions of ordinary differential equations by interval-symbolic methods
In the numerical estimation of the solution sets to differential equations with interval parameters, one of the major obstacles to the computation of good enclosures is known to be the so-called wrapping effect that causes exponential growth of the computed bounds of the solution. Up to now, this phenomenon has not been overcome yet. In the present paper, we advance a new explanation of the reasons of the wrapping effect relying on concepts of structural stability and recent developments in qualitative theory of differential equations. Additionally, we present the fundamentals of new interval-symbolic methods for the solution of interval differential equations, which sometimes enable one to successfully defeat the wrapping effect, and give a theoretical study of the new technique.
[full text] Classificator Msc2000:- *34A34 Nonlinear equations and systems, general
- 65G40 General methods in interval analysis
- 65L05 Initial value problems
- 65L07 Numerical investigation of stability of solutions
- 65L70 Error bounds
Classificator Computer Science:- *G.1.0 General (Numerical Analysis)
- G.1.7 Ordinary Differential Equations
Keywords: differential equations with an interval parameter, wrapping effect, qualitative theory of differential equations, interval-symbolic method, enclosure of solutions, error bounds
Author(s):
Rogalev Alexey Nikolaevich
PhD. , Associate Professor
Position: Associate Professor
Office: Institute of Computational Modelling SB RAS
Address: 660036, Russia, Krasnoyarsk, Akademgorodok, 50, p.44
E-mail: rogalyov@icm.krasn.ru
SPIN-code: 7519-8826Shokin Yuriy Ivanovich
Dr. , Academician RAS, Professor
Position: Scientific Director of the Institute
Office: Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave., 6
Phone Office: (383) 334 91 10
E-mail: shokin@ict.nsc.ru
SPIN-code: 6442-4180
Bibliography link:
Rogalev A.N., Shokin Y.I. Examining and estimating solutions of ordinary differential equations by interval-symbolic methods // Computational technologies. 1999. V. 4. ¹ 4. P. 51-75
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