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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2405.07727 |
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| _version_ | 1866913348302405632 |
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| author | Kepley, Shane de Wolff, Babette A. J. |
| author_facet | Kepley, Shane de Wolff, Babette A. J. |
| contents | Pseudospectral approximation provides a means to approximate the dynamics of delay differential equations (DDE) by ordinary differential equations (ODE). This article develops a computer-aided algorithm to determine the distance between the unstable manifold of a DDE and the unstable manifold of the approximating pseudospectral ODE. The algorithm is based upon the parametrization method. While a-priori the parametrization method for a vector-valued ODE involves computing a sequence of vector-valued Taylor coefficients, we show that for the pseudospectral ODE, due to its specific structure, the problem reduces to finding a sequence of scalars, which significantly simplifies the problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07727 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Validated error bounds for pseudospectral approximation of delay differential equations: unstable manifolds Kepley, Shane de Wolff, Babette A. J. Dynamical Systems Pseudospectral approximation provides a means to approximate the dynamics of delay differential equations (DDE) by ordinary differential equations (ODE). This article develops a computer-aided algorithm to determine the distance between the unstable manifold of a DDE and the unstable manifold of the approximating pseudospectral ODE. The algorithm is based upon the parametrization method. While a-priori the parametrization method for a vector-valued ODE involves computing a sequence of vector-valued Taylor coefficients, we show that for the pseudospectral ODE, due to its specific structure, the problem reduces to finding a sequence of scalars, which significantly simplifies the problem. |
| title | Validated error bounds for pseudospectral approximation of delay differential equations: unstable manifolds |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2405.07727 |