Representation of solutions of linear differential systems of second-order with constant delays
We derive representations for solutions to initial-value problems for n-dimensional second-order differential equations with delays, x''(t) = 2Ax' (t − τ ) − (A² + B² )x(t − 2τ), and x''(t) = (A + B)x' (t − τ ) − ABx(t − 2τ ), by means of special matrix delayed...
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| Дата: | 2016 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2016
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| Назва видання: | Нелінійні коливання |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/177245 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Representation of solutions of linear differential systems of second-order with constant delays / Z. Svoboda // Нелінійні коливання. — 2016. — Т. 19, № 1. — С. 129-141 — Бібліогр.: 32 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1772452021-02-14T01:26:13Z Representation of solutions of linear differential systems of second-order with constant delays Svoboda, Z. We derive representations for solutions to initial-value problems for n-dimensional second-order differential equations with delays, x''(t) = 2Ax' (t − τ ) − (A² + B² )x(t − 2τ), and x''(t) = (A + B)x' (t − τ ) − ABx(t − 2τ ), by means of special matrix delayed functions. Here A and B are commuting (n × n)-matrices and τ > 0. Moreover, a formula connecting delayed matrix exponential with delayed matrix sine and delayed matrix cosine is derived. We also discuss common features of the two considered equations. Знайдено зображення розв’язкiв задач iз початковими умовами для диференцiальних рiвнянь другого порядку розмiрностi n iз запiзненнями x''(t) = 2Ax' (t − τ ) − (A² + B² )x(t − 2τ), та x''(t) = (A + B)x' (t − τ ) − ABx(t − 2τ ), при цьому використано спецiальнi матричнi функцiї iз запiзненням. Тут A i B — комутативнi матрицi розмiрностi n × n i τ > 0. Також отримано формулу, що зв’язує експоненцiальну матрицю з запiзненням з sin- та cos-матрицями iз запiзненням. Також розглянуто загальнi властивостi обох розглядуваних рiвнянь. 2016 Article Representation of solutions of linear differential systems of second-order with constant delays / Z. Svoboda // Нелінійні коливання. — 2016. — Т. 19, № 1. — С. 129-141 — Бібліогр.: 32 назв. — англ. 1562-3076 http://dspace.nbuv.gov.ua/handle/123456789/177245 517.9 en Нелінійні коливання Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We derive representations for solutions to initial-value problems for n-dimensional second-order differential equations with delays,
x''(t) = 2Ax' (t − τ ) − (A² + B² )x(t − 2τ),
and
x''(t) = (A + B)x' (t − τ ) − ABx(t − 2τ ),
by means of special matrix delayed functions. Here A and B are commuting (n × n)-matrices and τ > 0. Moreover, a formula connecting delayed matrix exponential with delayed matrix sine and delayed matrix cosine is derived. We also discuss common features of the two considered equations. |
| format |
Article |
| author |
Svoboda, Z. |
| spellingShingle |
Svoboda, Z. Representation of solutions of linear differential systems of second-order with constant delays Нелінійні коливання |
| author_facet |
Svoboda, Z. |
| author_sort |
Svoboda, Z. |
| title |
Representation of solutions of linear differential systems of second-order with constant delays |
| title_short |
Representation of solutions of linear differential systems of second-order with constant delays |
| title_full |
Representation of solutions of linear differential systems of second-order with constant delays |
| title_fullStr |
Representation of solutions of linear differential systems of second-order with constant delays |
| title_full_unstemmed |
Representation of solutions of linear differential systems of second-order with constant delays |
| title_sort |
representation of solutions of linear differential systems of second-order with constant delays |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/177245 |
| citation_txt |
Representation of solutions of linear differential systems of second-order with constant delays / Z. Svoboda // Нелінійні коливання. — 2016. — Т. 19, № 1. — С. 129-141 — Бібліогр.: 32 назв. — англ. |
| series |
Нелінійні коливання |
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AT svobodaz representationofsolutionsoflineardifferentialsystemsofsecondorderwithconstantdelays |
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2023-10-18T22:43:08Z |
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2023-10-18T22:43:08Z |
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1796156251847000064 |