Numerical solutions for implicit differential equations with singularities
In this paper we introduce a technique to deal with implicit differential equations exhibiting singularities. Our approach is a geometrical one, we use the concept of contact structure on a manifold associated with the differential equation. In this setting we prove an existence and uniqueness theor...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Universidade Estadual de Londrina
2022-05-01
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| Series: | Semina: Ciências Exatas e Tecnológicas |
| Subjects: | |
| Online Access: | https://ojs.uel.br/revistas/uel/index.php/semexatas/article/view/45618 |
| _version_ | 1797951677002678272 |
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| author | Antonio Castelo Geovan Tavares Juliana Bertoco |
| author_facet | Antonio Castelo Geovan Tavares Juliana Bertoco |
| author_sort | Antonio Castelo |
| collection | DOAJ |
| description | In this paper we introduce a technique to deal with implicit differential equations exhibiting singularities. Our approach is a geometrical one, we use the concept of contact structure on a manifold associated with the differential equation. In this setting we prove an existence and uniqueness theorem. We also show how it relates to known geometric results for this kind of equation. We also indicate how the method can be implemented by using continuation methods techniques and the BDF (Backward Differentiation Formula). |
| first_indexed | 2024-04-10T22:34:21Z |
| format | Article |
| id | doaj.art-b811dec5252d47c9ae6984aaabf3eb29 |
| institution | Directory Open Access Journal |
| issn | 1676-5451 1679-0375 |
| language | English |
| last_indexed | 2024-04-10T22:34:21Z |
| publishDate | 2022-05-01 |
| publisher | Universidade Estadual de Londrina |
| record_format | Article |
| series | Semina: Ciências Exatas e Tecnológicas |
| spelling | doaj.art-b811dec5252d47c9ae6984aaabf3eb292023-01-16T15:53:08ZengUniversidade Estadual de LondrinaSemina: Ciências Exatas e Tecnológicas1676-54511679-03752022-05-01431Esp10.5433/1679-0375.2022v43n1Espp3Numerical solutions for implicit differential equations with singularitiesAntonio Castelo0Geovan Tavares1Juliana Bertoco2Universidade de São Paulo - USPPontifícia Universidade Católica de São Paulo - PUC-SPUniversidade de São Paulo - USPIn this paper we introduce a technique to deal with implicit differential equations exhibiting singularities. Our approach is a geometrical one, we use the concept of contact structure on a manifold associated with the differential equation. In this setting we prove an existence and uniqueness theorem. We also show how it relates to known geometric results for this kind of equation. We also indicate how the method can be implemented by using continuation methods techniques and the BDF (Backward Differentiation Formula).https://ojs.uel.br/revistas/uel/index.php/semexatas/article/view/45618Implicit differential equationsSingularitiesDifferential algebraic equations |
| spellingShingle | Antonio Castelo Geovan Tavares Juliana Bertoco Numerical solutions for implicit differential equations with singularities Semina: Ciências Exatas e Tecnológicas Implicit differential equations Singularities Differential algebraic equations |
| title | Numerical solutions for implicit differential equations with singularities |
| title_full | Numerical solutions for implicit differential equations with singularities |
| title_fullStr | Numerical solutions for implicit differential equations with singularities |
| title_full_unstemmed | Numerical solutions for implicit differential equations with singularities |
| title_short | Numerical solutions for implicit differential equations with singularities |
| title_sort | numerical solutions for implicit differential equations with singularities |
| topic | Implicit differential equations Singularities Differential algebraic equations |
| url | https://ojs.uel.br/revistas/uel/index.php/semexatas/article/view/45618 |
| work_keys_str_mv | AT antoniocastelo numericalsolutionsforimplicitdifferentialequationswithsingularities AT geovantavares numericalsolutionsforimplicitdifferentialequationswithsingularities AT julianabertoco numericalsolutionsforimplicitdifferentialequationswithsingularities |