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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| Опубліковано в: : | Український математичний вісник |
|---|---|
| Дата: | 2009 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2009
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/124362 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862745309964140544 |
|---|---|
| author | Bruno, A.D. Kudryashov, N.A. |
| author_facet | Bruno, A.D. Kudryashov, N.A. |
| 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. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| 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.
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| first_indexed | 2025-12-07T20:39:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-124362 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | English |
| last_indexed | 2025-12-07T20:39:45Z |
| publishDate | 2009 |
| publisher | Інститут прикладної математики і механіки НАН України |
| 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 |
| spellingShingle | Expansions of solutions to the equation P₁² by algorithms of power geometry Bruno, A.D. Kudryashov, N.A. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/124362 |
| work_keys_str_mv | AT brunoad expansionsofsolutionstotheequationp12byalgorithmsofpowergeometry AT kudryashovna expansionsofsolutionstotheequationp12byalgorithmsofpowergeometry |