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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2020, Volume 24, Number 1, Pages 174–186 (Mi vsgtu1727)  

Short Communication
Differential Equations and Mathematical Physics

On extension of the domain for analytical approximate solution of one class of nonlinear differential equations of the second order in a complex domain

V. N. Orlova*, T. Yu. Leontievab

a National Research Moscow State University of Civil Engineering, Moscow, 129337, Russian Federation
b SAPEI CR “Interregional Competence Centre – Cheboksary Electromechanical College” of the Ministry of Education and Youth Policy of the Chuvash Republic, Cheboksary, 428000, Russian Federation

Abstract: In previous research the authors have implemented the investigation of one class of nonlinear differential equations of the second order in the neighborhood of variable exceptional point. The authors have proven the following: the existence of variable exceptional point, theorem of the existence and uniqueness of solution in the neighborhood of variable exceptional point. The analytical approximated solution in the neighborhood of variable exceptional point was built. The authors researched the influence of disturbance of variable exceptional point on an approximated solution. The results obtained for the real domain have been extended to the complex domain $|z|<|\tilde z^*|\leqslant |z^*|$, where $z^*$ is precise value of variable exceptional point, $\tilde z^*$ is approximate value of variable exceptional point. In the present paper, the authors have carried out the investigation of analytical approximate solution of the influence of disturbance of variable exceptional point in the domain $|z|>|\tilde z^*|\geqslant |z^*|$, giving special attention to change of direction of movement along the beam towards the origin of coordinates of a complex domain. These researches are actual due to the variable exceptional point pattern (even fractional degree of critical pole). The received results are accompanied by the numerical experiment and complete the investigation of analytical approximated solution of the considered class of nonlinear differential equations in the neighborhood of variable exceptional point depending on the direction of movement along the beam in a complex domain.

Keywords: movable singular point, nonlinear differential equation, analytical approximate solution, neighborhood of variable exceptional point, complex domain, a posteriori estimate
* Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1727

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Bibliographic databases:

UDC: 517.928.4
MSC: 34M99
Received: July 26, 2019
Revised: February 7, 2020
Accepted: February 10, 2020
First online: March 10, 2020

Citation: V. N. Orlov, T. Yu. Leontieva, “On extension of the domain for analytical approximate solution of one class of nonlinear differential equations of the second order in a complex domain”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 24:1 (2020), 174–186

Citation in format AMSBIB
\Bibitem{OrlLeo20}
\by V.~N.~Orlov, T.~Yu.~Leontieva
\paper On extension of~the~domain for~analytical approximate solution of~one~class of~nonlinear differential equations of~the~second order in~a~complex domain
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2020
\vol 24
\issue 1
\pages 174--186
\mathnet{http://mi.mathnet.ru/vsgtu1727}
\crossref{https://doi.org/10.14498/vsgtu1727}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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