Rational general solutions of planar rational systems of autonomous ODEs()

In this paper, we provide an algorithm to compute explicit rational solutions of a rational system of autonomous ordinary differential equations (ODEs) from its rational invariant algebraic curves. The method is based on the proper rational parametrization of these curves and the fact that by linear...

Descripción completa

Detalles Bibliográficos
Autores principales: Châu Ngô, L.X., Winkler, Franz
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier Limited 2011
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4608394/
https://www.ncbi.nlm.nih.gov/pubmed/26538803
http://dx.doi.org/10.1016/j.jsc.2011.06.002
_version_ 1782395663204483072
author Châu Ngô, L.X.
Winkler, Franz
author_facet Châu Ngô, L.X.
Winkler, Franz
author_sort Châu Ngô, L.X.
collection PubMed
description In this paper, we provide an algorithm to compute explicit rational solutions of a rational system of autonomous ordinary differential equations (ODEs) from its rational invariant algebraic curves. The method is based on the proper rational parametrization of these curves and the fact that by linear reparametrizations, we can find the rational solutions of the given system of ODEs. Moreover, if the system has a rational first integral, we can decide whether it has a rational general solution and compute it in the affirmative case.
format Online
Article
Text
id pubmed-4608394
institution National Center for Biotechnology Information
language English
publishDate 2011
publisher Elsevier Limited
record_format MEDLINE/PubMed
spelling pubmed-46083942015-11-02 Rational general solutions of planar rational systems of autonomous ODEs() Châu Ngô, L.X. Winkler, Franz J Symb Comput Article In this paper, we provide an algorithm to compute explicit rational solutions of a rational system of autonomous ordinary differential equations (ODEs) from its rational invariant algebraic curves. The method is based on the proper rational parametrization of these curves and the fact that by linear reparametrizations, we can find the rational solutions of the given system of ODEs. Moreover, if the system has a rational first integral, we can decide whether it has a rational general solution and compute it in the affirmative case. Elsevier Limited 2011-10 /pmc/articles/PMC4608394/ /pubmed/26538803 http://dx.doi.org/10.1016/j.jsc.2011.06.002 Text en © 2011 Elsevier Ltd. https://creativecommons.org/licenses/by-nc-nd/3.0/This is an open access article under the CC BY NC ND license (https://creativecommons.org/licenses/by-nc-nd/3.0/).
spellingShingle Article
Châu Ngô, L.X.
Winkler, Franz
Rational general solutions of planar rational systems of autonomous ODEs()
title Rational general solutions of planar rational systems of autonomous ODEs()
title_full Rational general solutions of planar rational systems of autonomous ODEs()
title_fullStr Rational general solutions of planar rational systems of autonomous ODEs()
title_full_unstemmed Rational general solutions of planar rational systems of autonomous ODEs()
title_short Rational general solutions of planar rational systems of autonomous ODEs()
title_sort rational general solutions of planar rational systems of autonomous odes()
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4608394/
https://www.ncbi.nlm.nih.gov/pubmed/26538803
http://dx.doi.org/10.1016/j.jsc.2011.06.002
work_keys_str_mv AT chaungolx rationalgeneralsolutionsofplanarrationalsystemsofautonomousodes
AT winklerfranz rationalgeneralsolutionsofplanarrationalsystemsofautonomousodes

Ejemplares similares