Puiseux series solutions of ODEs
In this article, we will determine Puiseux series solutions of ordinary polynomial differential equations. We also study the binary complexity of computing such solutions. We will prove that this complexity bound is single exponential in the number of terms in the series. Our algorithm is based...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2015-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/135/abstr.html |
| _version_ | 1819080641785888768 |
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| author | Ali Ayad Ali Fares Youssef Ayyad Raafat Tarraf |
| author_facet | Ali Ayad Ali Fares Youssef Ayyad Raafat Tarraf |
| author_sort | Ali Ayad |
| collection | DOAJ |
| description | In this article, we will determine Puiseux series solutions of ordinary
polynomial differential equations. We also study the binary complexity of
computing such solutions.
We will prove that this complexity bound is single exponential in the number
of terms in the series. Our algorithm is based on a differential version
of the Newton-Puiseux procedure for algebraic equations. |
| first_indexed | 2024-12-21T19:48:07Z |
| format | Article |
| id | doaj.art-34be5df92fec461b847b2341f6bf4768 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-21T19:48:07Z |
| publishDate | 2015-05-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-34be5df92fec461b847b2341f6bf47682022-12-21T18:52:16ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-05-012015135,17Puiseux series solutions of ODEsAli Ayad0Ali Fares1Youssef Ayyad2Raafat Tarraf3 Lebanese univ., Hadath, Lebanon Lebanese univ., Hadath, Lebanon Lebanese univ., Hadath, Lebanon Lebanese univ., Hadath, Lebanon In this article, we will determine Puiseux series solutions of ordinary polynomial differential equations. We also study the binary complexity of computing such solutions. We will prove that this complexity bound is single exponential in the number of terms in the series. Our algorithm is based on a differential version of the Newton-Puiseux procedure for algebraic equations.http://ejde.math.txstate.edu/Volumes/2015/135/abstr.htmlSymbolic computationscomplexity analysis of algorithmsordinary polynomial differential equationsformal power seriesNewton polygons |
| spellingShingle | Ali Ayad Ali Fares Youssef Ayyad Raafat Tarraf Puiseux series solutions of ODEs Electronic Journal of Differential Equations Symbolic computations complexity analysis of algorithms ordinary polynomial differential equations formal power series Newton polygons |
| title | Puiseux series solutions of ODEs |
| title_full | Puiseux series solutions of ODEs |
| title_fullStr | Puiseux series solutions of ODEs |
| title_full_unstemmed | Puiseux series solutions of ODEs |
| title_short | Puiseux series solutions of ODEs |
| title_sort | puiseux series solutions of odes |
| topic | Symbolic computations complexity analysis of algorithms ordinary polynomial differential equations formal power series Newton polygons |
| url | http://ejde.math.txstate.edu/Volumes/2015/135/abstr.html |
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