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...
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| Видавець: | Інститут прикладної математики і механіки НАН України |
|---|---|
| Дата: | 2009 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2009
|
| Назва видання: | Український математичний вісник |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/124362 |
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| Цитувати: | 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-124362 |
|---|---|
| record_format |
dspace |
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irk-123456789-1243622017-09-25T03:02:56Z Expansions of solutions to the equation P₁² by algorithms of power geometry Bruno, A.D. Kudryashov, N.A. 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. 2009 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/124362 2000 MSC. 34E05, 41A58, 41A60. en Український математичний вісник Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Bruno, A.D. Kudryashov, N.A. |
| spellingShingle |
Bruno, A.D. Kudryashov, N.A. Expansions of solutions to the equation P₁² by algorithms of power geometry Український математичний вісник |
| author_facet |
Bruno, A.D. Kudryashov, N.A. |
| author_sort |
Bruno, A.D. |
| title |
Expansions of solutions to the equation P₁² by algorithms of power geometry |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Український математичний вісник |
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2023-10-18T20:46:15Z |
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2023-10-18T20:46:15Z |
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