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On One System of Ordinary Differential Equations of Large Dimension and a Delay Equation

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Abstract

We consider some system of ordinary differential equations modeling a multistage synthesis of a substance. We prove the global limit theorems that establish connections between the solutions to a system of ordinary differential equations of large dimension and the solutions to a delay equation. The obtained results enable us to find the approximate solutions to the systems under consideration of an arbitrarily high dimension on the whole half-axis. Some approximation estimates are established.

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Funding

The authors were supported by the Russian Foundation for Basic Research (project no. 18-29- 10086), The Development Program of the Federal State Autonomous Educational Institution of Higher Education Vernadsky Crimean Federal University for 2015-2024.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    G. V. Demidenko & I. A. Uvarova

  2. Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russia

    G. V. Demidenko & I. A. Uvarova

  3. V. I.Vernadsky Crimean Federal University, pr. Akad. Vernadskogo 4, Simferopol’, 295007, Russia

    Yu. A. Khazova

Authors
  1. G. V. Demidenko
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  2. I. A. Uvarova
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  3. Yu. A. Khazova
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Corresponding authors

Correspondence to G. V. Demidenko, I. A. Uvarova or Yu. A. Khazova.

Additional information

Russian Text © The Author(s), 2019, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2019, Vol. XXII, No. 3, pp. 59–73.

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Demidenko, G.V., Uvarova, I.A. & Khazova, Y.A. On One System of Ordinary Differential Equations of Large Dimension and a Delay Equation. J. Appl. Ind. Math. 13, 447–459 (2019). https://doi.org/10.1134/S1990478919030062

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  • DOI: https://doi.org/10.1134/S1990478919030062

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