On approximate implicit Taylor methods for ordinary differential equations
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910316769574912 |
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| author | Baeza, Antonio Bürger, Raimund Martí, María del Carmen Mulet, Pep Zorío, David |
| author_facet | Baeza, Antonio Bürger, Raimund Martí, María del Carmen Mulet, Pep Zorío, David |
| contents | An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a method that requires less evaluations of the function that defines the ODE and its derivatives than the usual version. On the other hand, an efficient numerical solution of the equation that arises from the discretization by means of Newton's method is introduced for an implicit scheme of any order. Numerical experiments illustrate that the resulting algorithm is simpler to implement and has better performance than its exact counterpart. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01473 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On approximate implicit Taylor methods for ordinary differential equations Baeza, Antonio Bürger, Raimund Martí, María del Carmen Mulet, Pep Zorío, David Numerical Analysis An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a method that requires less evaluations of the function that defines the ODE and its derivatives than the usual version. On the other hand, an efficient numerical solution of the equation that arises from the discretization by means of Newton's method is introduced for an implicit scheme of any order. Numerical experiments illustrate that the resulting algorithm is simpler to implement and has better performance than its exact counterpart. |
| title | On approximate implicit Taylor methods for ordinary differential equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2402.01473 |