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...
Збережено в:
| Дата: | 2016 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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. |
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