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Estimating the Coefficients of a System of Ordinary Differential Equations Based on Inaccurate Observations

Author

Listed:
  • Gurami Tsitsiashvili

    (Institute for Applied Mathematics, Far Eastern Branch of Russian Academy of Sciences, 690041 Vladivostok, Russia
    Current address: IAM FEB RAS, Radio Str. 7, 690041 Vladivostok, Russia.)

  • Marina Osipova

    (Institute for Applied Mathematics, Far Eastern Branch of Russian Academy of Sciences, 690041 Vladivostok, Russia
    Institute for Applied Mathematics, Far Eastern Federal University, 690922 Vladivostok, Russia)

  • Yury Kharchenko

    (Institute for Applied Mathematics, Far Eastern Branch of Russian Academy of Sciences, 690041 Vladivostok, Russia)

Abstract

In this paper, we solve the problem of estimating the parameters of a system of ordinary differential equations from observations on a short interval of argument values. By analogy with linear regression analysis, a sufficiently large number of observations are selected on this segment and the values of the functions on the right side of the system and the values of the derivatives are estimated. According to the obtained estimates, unknown parameters are determined, using the differential equations system. The consistency of the estimates obtained in this way is proved with an increase in the number of observations over a short period of argument values. Here, an algorithm for estimating parameters acts as a system. The error of the obtained estimate is an indicator of its quality. A sequence of inaccurate measurements is a random process. The method of linear regression analysis applied to an almost linear regression function is used as an optimization procedure.

Suggested Citation

  • Gurami Tsitsiashvili & Marina Osipova & Yury Kharchenko, 2022. "Estimating the Coefficients of a System of Ordinary Differential Equations Based on Inaccurate Observations," Mathematics, MDPI, vol. 10(3), pages 1-9, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:502-:d:742139
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    References listed on IDEAS

    as
    1. Yuping Hu & Siyu Wu & Sanying Feng & Junliang Jin, 2020. "Estimation in Partial Functional Linear Spatial Autoregressive Model," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
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    Cited by:

    1. Y. Villacampa & F. J. Navarro-González, 2022. "An Algorithm for Numerical Integration of ODE with Sampled Unknown Functional Factors," Mathematics, MDPI, vol. 10(9), pages 1-23, May.
    2. Gurami Tsitsiashvili & Alexandr Losev, 2022. "Safety Margin Prediction Algorithms Based on Linear Regression Analysis Estimates," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
    3. Gurami Tsitsiashvili & Alexey Gudimenko & Marina Osipova, 2023. "Mathematical and Statistical Aspects of Estimating Small Oscillations Parameters in a Conservative Mechanical System Using Inaccurate Observations," Mathematics, MDPI, vol. 11(12), pages 1-11, June.

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