Approximation method for the problems of mechanics of inhomogeneous hereditarily elastic bodies
We consider a boundary-value problem of mechanics of inhomogeneous hereditarily elastic bodies formulated as a linear equation with an operator of fractional integration, partial derivatives with respect to time and spatial variables, and polynomial-type coefficients of one of the variables. An appr...
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| Дата: | 1994 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1994
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5640 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511869844848640 |
|---|---|
| author | Sinaiskii, E. S. Синайський, Є. С. |
| author_facet | Sinaiskii, E. S. Синайський, Є. С. |
| author_sort | Sinaiskii, E. S. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:14:58Z |
| description | We consider a boundary-value problem of mechanics of inhomogeneous hereditarily elastic bodies formulated as a linear equation with an operator of fractional integration, partial derivatives with respect to time and spatial variables, and polynomial-type coefficients of one of the variables. An approximate solution of this problem is constructed according to Dzyadyk's a-method combined with the use of the Laplace transformation. It is proved that the errors of the approximation of the required function and its derivatives decrease in geometric progression. |
| first_indexed | 2026-03-24T03:19:45Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5640 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:19:45Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/f5/c3d82105a66475821ae6a13166e174f5.pdf |
| spelling | umjimathkievua-article-56402020-03-19T09:14:58Z Approximation method for the problems of mechanics of inhomogeneous hereditarily elastic bodies Аппроксимационный метод в задачах механики для неоднородных наследственно-упругих тел Sinaiskii, E. S. Синайський, Є. С. We consider a boundary-value problem of mechanics of inhomogeneous hereditarily elastic bodies formulated as a linear equation with an operator of fractional integration, partial derivatives with respect to time and spatial variables, and polynomial-type coefficients of one of the variables. An approximate solution of this problem is constructed according to Dzyadyk's a-method combined with the use of the Laplace transformation. It is proved that the errors of the approximation of the required function and its derivatives decrease in geometric progression. A boundary-value problem is considered for an inhomogeneous heredirarily elastic body. This problem is formulated in terms of a linear equation with an operator of fractional integration, partial derivatives with respect to time and space variables, and coefficients of polynomial type in one of the variables. An approximate solution of the problem is constructed by using Dzyadyk's a-method and the Laplace transformation. It is proved that the approximation error of the function and its derivatives decreases in geometric progression. Institute of Mathematics, NAS of Ukraine 1994-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5640 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 9 (1994); 1234–1245 Український математичний журнал; Том 46 № 9 (1994); 1234–1245 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5640/7965 https://umj.imath.kiev.ua/index.php/umj/article/view/5640/7966 Copyright (c) 1994 Sinaiskii E. S. |
| spellingShingle | Sinaiskii, E. S. Синайський, Є. С. Approximation method for the problems of mechanics of inhomogeneous hereditarily elastic bodies |
| title | Approximation method for the problems of mechanics of inhomogeneous hereditarily elastic bodies |
| title_alt | Аппроксимационный метод в задачах механики для неоднородных наследственно-упругих тел |
| title_full | Approximation method for the problems of mechanics of inhomogeneous hereditarily elastic bodies |
| title_fullStr | Approximation method for the problems of mechanics of inhomogeneous hereditarily elastic bodies |
| title_full_unstemmed | Approximation method for the problems of mechanics of inhomogeneous hereditarily elastic bodies |
| title_short | Approximation method for the problems of mechanics of inhomogeneous hereditarily elastic bodies |
| title_sort | approximation method for the problems of mechanics of inhomogeneous hereditarily elastic bodies |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5640 |
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