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Solutions of ODEs with Removable Singularities-
incollection
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Area
Ordinary Differential Equations |
Author(s)
Harley Flanders
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Published in
Automatic Differentiation: Applications, Theory, and Implementations
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Editor(s)
H. M. Bücker, G. Corliss, P. Hovland, U. Naumann, B. Norris |
Year
2005 |
Publisher
Springer |
Abstract
We discuss explicit ODEs of the form \dotx=R(t,x), where R is a polynomial or rational function, and the solution x(t) has a removable singularity. We are particularly interested in functions built from elementary functions, such as x(t)=t/sin t. We also consider implicit ODEs of the forms P(t,x,\dotx)=0 and P(t,x,\dotx,\ddotx)=0. |
Cross-References
Bucker2005ADA |
BibTeX
@INCOLLECTION{
Flanders2005SoO,
author = "Harley Flanders",
title = "Solutions of {ODE}s with Removable Singularities",
editor = "H. M. B{\"u}cker and G. Corliss and P. Hovland and U. Naumann and B.
Norris",
booktitle = "Automatic Differentiation: {A}pplications, Theory, and Implementations",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer",
year = "2005",
abstract = "We discuss explicit ODEs of the form $\dot{x}=R(t,x)$, where $R$ is a
polynomial or rational function, and the solution $x(t)$ has a removable singularity. We are
particularly interested in functions built from elementary functions, such as
$x(t)=t/\sin\,t$. We also consider implicit ODEs of the forms $P(t,x,\dot{x})=0$ and
$P(t,x,\dot{x},\ddot{x})=0$.",
crossref = "Bucker2005ADA",
ad_area = "Ordinary Differential Equations",
pages = "35--45",
doi = "10.1007/3-540-28438-9_3"
}
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