Publication: Application of AD to a Family of Periodic Functions
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Application of AD to a Family of Periodic Functions

- incollection -
 

Author(s)
Harley Flanders

Published in
Automatic Differentiation of Algorithms: From Simulation to Optimization

Editor(s)
George Corliss, Christèle Faure, Andreas Griewank, Laurent Hascoët, Uwe Naumann

Year
2002

Publisher
Springer

Abstract
We study the initial value problem (IVP) for the system dx/dt=-ym, dy/dt=xn, where m and n are positive odd integers, x(0)=1, y(0)=0. Its solutions are periodic, and we find relations between the periods. Automatic differentiation is used to enable interesting mathematical explorations.

Cross-References
Corliss2002ADo

BibTeX
@INCOLLECTION{
         Flanders2002AoA,
       author = "Harley Flanders",
       title = "Application of AD to a Family of Periodic Functions",
       pages = "319--326",
       chapter = "38",
       crossref = "Corliss2002ADo",
       booktitle = "Automatic Differentiation of Algorithms: From Simulation to Optimization",
       year = "2002",
       editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent
         Hasco{\"e}t and Uwe Naumann",
       series = "Computer and Information Science",
       publisher = "Springer",
       address = "New York, NY",
       abstract = "We study the initial value problem (IVP) for the system $dx/dt=-y^{m}$,
         $dy/dt=x^{n}$, where $m$ and $n$ are positive odd integers, $x(0)=1$, $y(0)=0$. Its solutions are
         periodic, and we find relations between the periods. Automatic differentiation is used to enable
         interesting mathematical explorations."
}


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