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An Algorithm for Numerical Integration of ODE with Sampled Unknown Functional Factors

Author

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  • Y. Villacampa

    (Department of Applied Mathematics, University of Alicante, 03690 San Vicente del Raspeig, Spain)

  • F. J. Navarro-González

    (Department of Applied Mathematics, University of Alicante, 03690 San Vicente del Raspeig, Spain)

Abstract

The problem of having ordinary differential equations (ODE) whose coefficients are unknown functions is frequent in several fields. Sometimes, it is possible to obtain samples of the values of these functions in different instants or spatial points. The present paper presents a methodology for the numeric solving of these ODE. There are approximations to the problem for specific cases of equations, especially in the case where the parameters correspond to constants. Other studies focus on the case in which the functions under consideration are linear or meet a certain condition. There are two main advantages of the proposed algorithm. First, it does not impose any condition over the data or the subsequent function from where these sample data are derived. Additionally, the methodology used in the functions modeling can control the possibility of overfitting in the function modeling. This is a crucial point in order to limit the influence of model biases in the numerical solution of the ordinary differential equation under study.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1516-:d:807406
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    References listed on IDEAS

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    2. J. Cao & L. Wang & J. Xu, 2011. "Robust Estimation for Ordinary Differential Equation Models," Biometrics, The International Biometric Society, vol. 67(4), pages 1305-1313, December.
    3. Hulin Wu & Hongqi Xue & Arun Kumar, 2012. "Numerical Discretization-Based Estimation Methods for Ordinary Differential Equation Models via Penalized Spline Smoothing with Applications in Biomedical Research," Biometrics, The International Biometric Society, vol. 68(2), pages 344-352, June.
    4. Massiani, Jérôme & Gohs, Andreas, 2015. "The choice of Bass model coefficients to forecast diffusion for innovative products: An empirical investigation for new automotive technologies," Research in Transportation Economics, Elsevier, vol. 50(C), pages 17-28.
    5. 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.
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