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Publication detail
SVOBODA, Z.
Original Title
Representation of Solutions of Linear Differential Systems of the Second Order with Constant Delays
Type
journal article in Scopus
Language
English
Original Abstract
We deduce representations for the solutions of initial-value problems for n-dimensional differential equations of the second order with delays:x″(t)=2Ax′(t−τ)−(A2+B2)x(t−2τ) and x″(t)=(A+B)x′(t−τ)−ABx(t−2τ) by using special delay matrix functions. Here, A and B are commuting (n × n)-matrices and τ > 0. Moreover, a formula connecting the delay matrix exponential function with delayed matrix sine and delayed matrix cosine is obtained. We also discuss common features of the considered equations
Keywords
representation of solutions; delay; matrix delayed functions.
Authors
Released
1. 4. 2017
Publisher
Springer New York LLC
Location
New York US.
ISBN
1072-3374
Periodical
Journal of Mathematical Sciences
Year of study
222
Number
3
State
United States of America
Pages from
345
Pages to
358
Pages count
14
BibTex
@article{BUT143601, author="Zdeněk {Svoboda}", title="Representation of Solutions of Linear Differential Systems of the Second Order with Constant Delays", journal="Journal of Mathematical Sciences", year="2017", volume="222", number="3", pages="345--358", doi="10.1007/s10958-017-3304-9", issn="1072-3374" }