A Linear Prelle-Singer method
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909201013407744 |
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| author | Duarte, L. G. S. Ferreira, H. S. da Mota, L. A. C. P. |
| author_facet | Duarte, L. G. S. Ferreira, H. S. da Mota, L. A. C. P. |
| contents | The Prelle-Singer method allows determining an elementary first integral admitted by a polynomial vector field in the plane. It is a semi-algorithm whose nonlinear step consists of determining the Darboux polynomials of the vector field. In this article we construct a linear procedure to determine the Darboux polynomials present in the integrating factor of a polynomial vector field in the plane. Next, we extend the procedure to deal with rational 2ODEs that admit an elementary first integral |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_07912 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Linear Prelle-Singer method Duarte, L. G. S. Ferreira, H. S. da Mota, L. A. C. P. Mathematical Physics Exactly Solvable and Integrable Systems Computational Physics 34-XX G.1.7 The Prelle-Singer method allows determining an elementary first integral admitted by a polynomial vector field in the plane. It is a semi-algorithm whose nonlinear step consists of determining the Darboux polynomials of the vector field. In this article we construct a linear procedure to determine the Darboux polynomials present in the integrating factor of a polynomial vector field in the plane. Next, we extend the procedure to deal with rational 2ODEs that admit an elementary first integral |
| title | A Linear Prelle-Singer method |
| topic | Mathematical Physics Exactly Solvable and Integrable Systems Computational Physics 34-XX G.1.7 |
| url | https://arxiv.org/abs/2405.07912 |