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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2023, Volume 27, Number 2, Pages 357–374
DOI: https://doi.org/10.14498/vsgtu1978 (Mi vsgtu1978) 		 
Mathematical Modeling, Numerical Methods and Software Complexes

The estimation of solutions sets of linear systems of ordinary differential equations with perturbations based on the Cauchy operator

A. A. Rogalev

Institute of Space and Information Technologies, Siberian Federal University, Krasnoyarsk, 660074, Russian Federation
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DOI: https://doi.org/10.14498/vsgtu1978
Abstract: The paper outlines a method for numerical analysis of sets of solutions for linear systems of ordinary differential equations that contain perturbations in the right-hand side. The method determines extreme values of the solutions, which comprise the sets of solutions along the coordinate axes or in a specified direction. The estimations are based on using the Cauchy operator, written with symbolic formulas for variations of arbitrary constants. Additionally, control is implemented over the deviation of solutions when calculating a bundle of trajectories. The paper also is devoted to examples of estimating reachability sets of systems under the influence of control and disturbance effects.
Keywords: perturbations, trajectories tube, solutions sets, symbolic algorithms, symbolic formulae.
Funding agency Grant number
Russian Foundation for Basic Research 20-41-240002
The work was carried out within the framework of a project supported by grant no. 20–41–240002 provided by the RFBR, the Government of the Krasnoyarsk Territory, and the Regional Science Foundation.
Received: December 30, 2022
Revised: April 14, 2023
Accepted: May 25, 2023
First online: June 23, 2023
Bibliographic databases:
Document Type: Article
UDC: 517.925
MSC: 65L05, 65L07, 65G40, 34A34, 65L70
Language: Russian
Citation: A. A. Rogalev, “The estimation of solutions sets of linear systems of ordinary differential equations with perturbations based on the Cauchy operator”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 27:2 (2023), 357–374
Citation in format AMSBIB
\Bibitem{Rog23}
\by A.~A.~Rogalev
\paper The estimation of solutions sets of~linear systems of~ordinary differential equations with perturbations based on~the Cauchy operator
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2023
\vol 27
\issue 2
\pages 357--374
\mathnet{http://mi.mathnet.ru/vsgtu1978}
\crossref{https://doi.org/10.14498/vsgtu1978}
\edn{https://elibrary.ru/MXEZAB}
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