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Least-Squares Method in the Theory of Nonlinear Boundary-Value Problems Unsolved with Respect to the Derivative

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Ukrainian Mathematical Journal Aims and scope

We establish constructive necessary and sufficient conditions of solvability and propose a scheme for the construction of solutions to a nonlinear boundary-value problem unsolved with respect to the derivative. We also suggest convergent iterative schemes for finding approximate solutions of this problem. As an example of application of the proposed iterative scheme, we find approximations to the solutions of periodic boundary-value problems for a Rayleigh-type equation unsolved with respect to the derivative, in particular, in the case of a periodic problem for the equation used to describe the motion of satellites on elliptic orbits.

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Authors and Affiliations

  1. Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

    P. Benner & S. Chuiko

  2. Donbas State Pedagogical University, Sloviansk, Donetsk Region, Ukraine

    S. Chuiko

  3. Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Sloviansk, Donetsk Region, Ukraine

    O. Nesmelova

Authors
  1. P. Benner
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  2. S. Chuiko
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  3. O. Nesmelova
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Corresponding author

Correspondence to S. Chuiko.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 1, pp. 38–51, January, 2023. Ukrainian https://doi.org/10.37863/umzh.v75i1.7408.

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Benner, P., Chuiko, S. & Nesmelova, O. Least-Squares Method in the Theory of Nonlinear Boundary-Value Problems Unsolved with Respect to the Derivative. Ukr Math J 75, 40–55 (2023). https://doi.org/10.1007/s11253-023-02184-9

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  • DOI: https://doi.org/10.1007/s11253-023-02184-9

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