Representation of Green’s functions of the wave equation on a segment in finite terms
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...
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| Format: | Article |
| Language: | English |
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Saratov State University
2022-11-01
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| Series: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
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| Online Access: | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2022/11/430-446-malyshev.pdf |
| _version_ | 1798016684455362560 |
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| author | Malyshev, Ksaverii Yurievich |
| author_facet | Malyshev, Ksaverii Yurievich |
| author_sort | Malyshev, Ksaverii Yurievich |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T15:54:36Z |
| format | Article |
| id | doaj.art-66561813d2a94b458bd2271cc042ecbe |
| institution | Directory Open Access Journal |
| issn | 1816-9791 2541-9005 |
| language | English |
| last_indexed | 2024-04-11T15:54:36Z |
| publishDate | 2022-11-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| spelling | doaj.art-66561813d2a94b458bd2271cc042ecbe2022-12-22T04:15:13ZengSaratov State UniversityИзвестия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика1816-97912541-90052022-11-0122443044610.18500/1816-9791-2022-22-4-430-446Representation of Green’s functions of the wave equation on a segment in finite termsMalyshev, Ksaverii Yurievich0Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics (SINP MSU), 1(2) Leninskie gory, GSP-1, Moscow 119991, RussiaSolutions 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.https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2022/11/430-446-malyshev.pdfequation of oscillations on a segmentgreen’s functionrepresentation in finite termsboundary conditionsa. n. krylov’s method |
| spellingShingle | Malyshev, Ksaverii Yurievich Representation of Green’s functions of the wave equation on a segment in finite terms Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика equation of oscillations on a segment green’s function representation in finite terms boundary conditions a. n. krylov’s method |
| title | Representation of Green’s functions of the wave equation on a segment in finite terms |
| title_full | Representation of Green’s functions of the wave equation on a segment in finite terms |
| title_fullStr | Representation of Green’s functions of the wave equation on a segment in finite terms |
| title_full_unstemmed | Representation of Green’s functions of the wave equation on a segment in finite terms |
| title_short | Representation of Green’s functions of the wave equation on a segment in finite terms |
| title_sort | representation of green s functions of the wave equation on a segment in finite terms |
| topic | equation of oscillations on a segment green’s function representation in finite terms boundary conditions a. n. krylov’s method |
| url | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2022/11/430-446-malyshev.pdf |
| work_keys_str_mv | AT malyshevksaveriiyurievich representationofgreensfunctionsofthewaveequationonasegmentinfiniteterms |