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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2014, Volume 14, Issue 3, Pages 29–42 (Mi vngu343)  

Identification and Discretization of the Linear Differential Equations with Constant Coefficients

A. O. Egorshin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: In the first part of the article the problem and methods of solving the approximation and identification variational problems of the finite sequence have been stated. The method proposed is based on applying the dynamic models of the sequences under study. The peculiarities of using the models for such types of problems in the form of the ordinary linear difference equations with constant or maybe unknown coefficients have been shown here. In the second part, some problems of the discretization of the differential equations by means of the proposed problem of identification are studied. It is realized by obtaining an exact difference description of the differential equations solutions on the uniform net on the finite interval. Also, well-known analytical and proposed variational methods of the uniform discretization have been considered and compared here. With the use of the variational discretization it is not necessary to know differential coefficients. The conditions for realizing differential equations solutions on the net have been studied. Necessary and sufficient conditions for the uniqueness of the variational discretization and identification have been obtained. It is shown that under these conditions the results of the analytical and variational discretization coincide.

Keywords: variational approximation and identbfication, orthogonal projection, differential equation discretization, Gamilton–Kayley theorem, characteristic polynomial, corner subspace.

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English version:
Journal of Mathematical Sciences, 2016, 213:6, 844–856

UDC: 925.54:517.962.27
Received: 27.06.2013

Citation: A. O. Egorshin, “Identification and Discretization of the Linear Differential Equations with Constant Coefficients”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 14:3 (2014), 29–42; J. Math. Sci., 213:6 (2016), 844–856

Citation in format AMSBIB
\Bibitem{Ego14}
\by A.~O.~Egorshin
\paper Identification and Discretization of the Linear Differential Equations with Constant Coefficients
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2014
\vol 14
\issue 3
\pages 29--42
\mathnet{http://mi.mathnet.ru/vngu343}
\transl
\jour J. Math. Sci.
\yr 2016
\vol 213
\issue 6
\pages 844--856
\crossref{https://doi.org/10.1007/s10958-016-2746-9}


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  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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