Least-squares method in the theory of nonlinear boundary-value problems unsolved with respect to the derivative

P.  Benner; S.  Chuiko; O.  Nesmelova

doi:10.37863/umzh.v75i1.7408

P. Benner Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany https://orcid.org/0000-0003-3362-4103
S. Chuiko Donbas State Pedagogical Univ., Ukraine, Donetsk region, Sloviansk, and Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany https://orcid.org/0000-0001-7186-0129
O. Nesmelova Inst. Appl. Math. and Mech. Nat. Acad. Sci. Ukraine, Donetsk region, Sloviansk

DOI: https://doi.org/10.37863/umzh.v75i1.7408

Keywords: Nonlinear boundary-value problem unsolved with respect to the derivative; least squares method; constructive necessary and sufficient conditions; сonvergent iterative schemes

Abstract

UDC 517.9

We establish constructive necessary and sufficient conditions of solvability and a scheme for the construction of solutions for 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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