Computing Divisors and Common Multiples of Quasi-linear Ordinary Differential Equations

If solutions of a non-linear differential equation may be obtained by specialization of solutions of another equation we say that the former equation is a generalized divisor of the latter one. We design an algorithm which finds first-order quasi-linear generalized divisors of a second-order quasi-l...

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Published inComputer Algebra in Scientific Computing Vol. 8136; pp. 140 - 147
Main Authors Grigoriev, Dima, Schwarz, Fritz
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2013
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
divisor of equations
multiple of equations
quasi-linear ordinary differential equations
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Abstract If solutions of a non-linear differential equation may be obtained by specialization of solutions of another equation we say that the former equation is a generalized divisor of the latter one. We design an algorithm which finds first-order quasi-linear generalized divisors of a second-order quasi-linear ordinary differential equation. If solutions of an equation contain solutions of a pair of equations we say that the equation is a common multiple of the pair. We prove that a quasi-linear common multiple of a pair of quasi-linear equations always exists and design an algorithm which yields a quasi-linear common multiple.
AbstractList If solutions of a non-linear differential equation may be obtained by specialization of solutions of another equation we say that the former equation is a generalized divisor of the latter one. We design an algorithm which finds first-order quasi-linear generalized divisors of a second-order quasi-linear ordinary differential equation. If solutions of an equation contain solutions of a pair of equations we say that the equation is a common multiple of the pair. We prove that a quasi-linear common multiple of a pair of quasi-linear equations always exists and design an algorithm which yields a quasi-linear common multiple.
Author Grigoriev, Dima
Schwarz, Fritz
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Snippet If solutions of a non-linear differential equation may be obtained by specialization of solutions of another equation we say that the former equation is a...
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StartPage 140
SubjectTerms divisor of equations
multiple of equations
quasi-linear ordinary differential equations
Title Computing Divisors and Common Multiples of Quasi-linear Ordinary Differential Equations
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