Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Malyshev K. Y. Representation of Green’s functions of the wave equation on a segment in finite terms. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2022, vol. 22, iss. 4, pp. 430-446. DOI: 10.18500/1816-9791-2022-22-4-430-446, EDN: UIUDUP

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.11.2022
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Russian
Heading: 
Mathematics
Article type: 
Article
UDC: 
517.98
DOI: 
10.18500/1816-9791-2022-22-4-430-446
EDN: 
UIUDUP

Representation of Green’s functions of the wave equation on a segment in finite terms

Autors: 
Malyshev Ksaverii Yurievich, Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics (SINP MSU)
Abstract: 

Solutions of initial-boundary value problems on the excitation of oscillations of a finite segment by an instantaneous point sourse are investigated. Solutions to these problems, called Green's functions of the equation of oscillations on a segment, are known in the form of infinite Fourier series or series in terms of Heaviside functions. A. N. Krylov's method of accelerating the convergence of Fourier series for several types of boundary conditions not only accelerates the convergence, but allows one to compose expressions for Green's functions in finite terms. In this paper, finite expressions of Green's functions are given in the form of elementary functions of a real variable. Four different formulations of boundary conditions are considered, including the periodicity conditions.

Key words: 
equation of oscillations on a segment
Green’s function
representation in finite terms
boundary conditions
A. N. Krylov’s method
Acknowledgments: 
This work was supported by the RUDN University Strategic Academic Leadership Program. The author thanks Prof. M. D. Malykh (RUDN), for constant attention to the work, Prof. A. N. Bogolyubov (Faculty of Physics, Lomonosov Moscow State University), Prof. L. A. Sevastyanov (RUDN), M. V. Alekseev (HSE) for valuable discussions.
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Received: 
17.06.2022
Accepted: 
05.08.2022
Published: 
30.11.2022
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