A Tree Combinatorial Structure on the Solution of a Delay Differential Equation: A Generating Function Approach

This paper introduces a new approach for obtaining explicit solutions for a first order linear delay differential equation with constant coefficients. We conjecture that there is a generating function defined over of a specific class of polynomials in the delay that solves the equation, and prove in...

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Published inNumerical Analysis and Applied Mathematics (AIP Conference Proceedings Volmue 1048) Vol. 1048; pp. 118 - 121
Main Authors Fabiao, M Fatima, Brito, Paulo B, Staubyn, Antonio
Format Journal Article
LanguageEnglish
Published 01.01.2008
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ISBN073540576X
9780735405769
ISSN0094-243X
DOI10.1063/1.2990869

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Summary:This paper introduces a new approach for obtaining explicit solutions for a first order linear delay differential equation with constant coefficients. We conjecture that there is a generating function defined over of a specific class of polynomials in the delay that solves the equation, and prove in the main theorem that the conjecture is valid. We also show the advantage of our method as regards the traditional Method of Step Algorithm (MSA).
Bibliography:SourceType-Scholarly Journals-2
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ISBN:073540576X
9780735405769
ISSN:0094-243X
DOI:10.1063/1.2990869