Expansions of solutions to the equation P₁² by algorithms of power geometry
Algorithms of Power Geometry allow to find all power expansions of solutions to ordinary differential equations of a rather general type. Among these, there are Painlev´e equations and their generalizations. In the article we demonstrate how to find by these algorithms all power expansions of soluti...
Gespeichert in:
| Veröffentlicht in: | Український математичний вісник |
|---|---|
| Datum: | 2009 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2009
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/124362 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Expansions of solutions to the equation P₁² by algorithms of power geometry / A.D. Bruno, N.A. Kudryashov // Український математичний вісник. — 2009. — Т. 6, № 3. — С. 311-337. — Бібліогр.: 48 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-124362 |
|---|---|
| record_format |
dspace |
| spelling |
Bruno, A.D. Kudryashov, N.A. 2017-09-24T13:01:38Z 2017-09-24T13:01:38Z 2009 Expansions of solutions to the equation P₁² by algorithms of power geometry / A.D. Bruno, N.A. Kudryashov // Український математичний вісник. — 2009. — Т. 6, № 3. — С. 311-337. — Бібліогр.: 48 назв. — англ. 1810-3200 https://nasplib.isofts.kiev.ua/handle/123456789/124362 2000 MSC. 34E05, 41A58, 41A60. Algorithms of Power Geometry allow to find all power expansions of solutions to ordinary differential equations of a rather general type. Among these, there are Painlev´e equations and their generalizations. In the article we demonstrate how to find by these algorithms all power expansions of solutions to the equation P₁² at the points z = 0 and z = ∞. Two levels of the exponential additions to the expansions of solutions near z = ∞ are computed. We also describe an algorithm of computation of a basis of a minimal lattice containing a given set. en Інститут прикладної математики і механіки НАН України Український математичний вісник Expansions of solutions to the equation P₁² by algorithms of power geometry Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Expansions of solutions to the equation P₁² by algorithms of power geometry |
| spellingShingle |
Expansions of solutions to the equation P₁² by algorithms of power geometry Bruno, A.D. Kudryashov, N.A. |
| title_short |
Expansions of solutions to the equation P₁² by algorithms of power geometry |
| title_full |
Expansions of solutions to the equation P₁² by algorithms of power geometry |
| title_fullStr |
Expansions of solutions to the equation P₁² by algorithms of power geometry |
| title_full_unstemmed |
Expansions of solutions to the equation P₁² by algorithms of power geometry |
| title_sort |
expansions of solutions to the equation p₁² by algorithms of power geometry |
| author |
Bruno, A.D. Kudryashov, N.A. |
| author_facet |
Bruno, A.D. Kudryashov, N.A. |
| publishDate |
2009 |
| language |
English |
| container_title |
Український математичний вісник |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
Algorithms of Power Geometry allow to find all power expansions of solutions to ordinary differential equations of a rather general type. Among these, there are Painlev´e equations and their generalizations. In the article we demonstrate how to find by these algorithms all power expansions of solutions to the equation P₁² at the points z = 0 and z = ∞. Two levels of the exponential additions to the expansions of solutions near z = ∞ are computed. We also describe an algorithm of computation of a basis of a minimal lattice containing a given set.
|
| issn |
1810-3200 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/124362 |
| citation_txt |
Expansions of solutions to the equation P₁² by algorithms of power geometry / A.D. Bruno, N.A. Kudryashov // Український математичний вісник. — 2009. — Т. 6, № 3. — С. 311-337. — Бібліогр.: 48 назв. — англ. |
| work_keys_str_mv |
AT brunoad expansionsofsolutionstotheequationp12byalgorithmsofpowergeometry AT kudryashovna expansionsofsolutionstotheequationp12byalgorithmsofpowergeometry |
| first_indexed |
2025-12-07T20:39:45Z |
| last_indexed |
2025-12-07T20:39:45Z |
| _version_ |
1850883425945255936 |