Representation of solutions of systems of linear differential equations with multiple delays and nonpermutable variable coefficients

Solutions of nonhomogeneous systems of linear differential equations with multiple constant delays are explicitly stated without a commutativity assumption on the matrix coefficients. In comparison to recent results, the new formulas are not inductively built, but depend on a sum of noncommutative p...

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Bibliographic Details
Published inMathematical modelling and analysis Vol. 25; no. 2; pp. 303 - 322
Main Author Pospisil, Michal
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 01.03.2020
Subjects
Backup software
Cauchy problems
Coefficients
Commutativity
Differential equations
Laplace transform
Mathematical analysis
matrix polynomial
multiple delays
noncommutative product
nonhomogeneous equation
Representations
Time
Time dependence
noncommutative product
multiple delays
nonhomogeneous equation
Laplace transform
matrix polynomial
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Summary:Solutions of nonhomogeneous systems of linear differential equations with multiple constant delays are explicitly stated without a commutativity assumption on the matrix coefficients. In comparison to recent results, the new formulas are not inductively built, but depend on a sum of noncommutative products in the case of constant coefficients, or on a sum of iterated integrals in the case of time-dependent coefficients. This approach shall be more suitable for applications. Representation of a solution of a Cauchy problem for a system of higher order delay differential equations is also given.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2020.11194