Boundary-layer averaging for standard systems with lag
The $k$-th-order asymptotic solution of a standard system with lag is constructed along trajectories calculated according to the averaging scheme of A. N. Filatov. If the perturbation parameter $ε ≪ 1$, then the use of the step method for finding the solution is connected with cumbersome calculation...
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| Date: | 1994 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1994
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5614 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511843762569216 |
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| author | Efendiev, V. V. Zheltikov, V. P. Эфендиев, В. В. Желтиков, В. П. Эфендиев, В. В. Желтиков, В. П. |
| author_facet | Efendiev, V. V. Zheltikov, V. P. Эфендиев, В. В. Желтиков, В. П. Эфендиев, В. В. Желтиков, В. П. |
| author_sort | Efendiev, V. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:14:35Z |
| description | The $k$-th-order asymptotic solution of a standard system with lag is constructed along trajectories calculated according to the averaging scheme of A. N. Filatov. If the perturbation parameter $ε ≪ 1$, then the use of the step method for finding the solution is connected with cumbersome calculations because the number of required steps is inversely proportional to $ε$. We suggest another approach in which the step method is used only $k$ times for $t \in [0,k]$ and justify the asymptotic method. |
| first_indexed | 2026-03-24T03:19:20Z |
| format | Article |
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| id | umjimathkievua-article-5614 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:19:20Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/e7/37a6d2c43d3fdcfef4ab6f290b77f1e7.pdf |
| spelling | umjimathkievua-article-56142020-03-19T09:14:35Z Boundary-layer averaging for standard systems with lag Погранслойное усреднение систем стандартного вида с запаздыванием Efendiev, V. V. Zheltikov, V. P. Эфендиев, В. В. Желтиков, В. П. Эфендиев, В. В. Желтиков, В. П. The $k$-th-order asymptotic solution of a standard system with lag is constructed along trajectories calculated according to the averaging scheme of A. N. Filatov. If the perturbation parameter $ε ≪ 1$, then the use of the step method for finding the solution is connected with cumbersome calculations because the number of required steps is inversely proportional to $ε$. We suggest another approach in which the step method is used only $k$ times for $t \in [0,k]$ and justify the asymptotic method. Вздовж траєкторій, які вирахувані за схемами усереднення О. М. Філатова, побудовано асимптотичний розв’язок порядку $k$ системи стандартного вигляду із запізненням. Якщо параметр збурення $ε ≪ 1$, то розв’язування методом кроків вимагає великого об’єму обчислень, оскільки кількість кроків обернено пропорціональна $ε$. Запропоновано інший підхід, який використовує метод кроків тільки $k$ разів для $t \in [0,k]$. Institute of Mathematics, NAS of Ukraine 1994-10-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5614 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 10 (1994); 1362–1368 Український математичний журнал; Том 46 № 10 (1994); 1362–1368 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5614/7913 https://umj.imath.kiev.ua/index.php/umj/article/view/5614/7914 Copyright (c) 1994 Efendiev V. V.; Zheltikov V. P. |
| spellingShingle | Efendiev, V. V. Zheltikov, V. P. Эфендиев, В. В. Желтиков, В. П. Эфендиев, В. В. Желтиков, В. П. Boundary-layer averaging for standard systems with lag |
| title | Boundary-layer averaging for standard systems with lag |
| title_alt | Погранслойное усреднение систем стандартного вида с запаздыванием |
| title_full | Boundary-layer averaging for standard systems with lag |
| title_fullStr | Boundary-layer averaging for standard systems with lag |
| title_full_unstemmed | Boundary-layer averaging for standard systems with lag |
| title_short | Boundary-layer averaging for standard systems with lag |
| title_sort | boundary-layer averaging for standard systems with lag |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5614 |
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