Boundary-value problems of functional differential equations with state-dependent delays
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915587599368192 |
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| author | andò, Alessia Sieber, Jan |
| author_facet | andò, Alessia Sieber, Jan |
| contents | We prove convergence of piecewise polynomial collocation methods applied to periodic boundary value problems for functional differential equations with state-dependent delays. The state dependence of the delays leads to nonlinearities that are not locally Lipschitz continuous preventing the direct application of general abstract discretization theoretic frameworks. We employ a weaker form of differentiability, which we call mild differentiability, to prove that a locally unique solution of the functional differential equation is approximated by the solution of the discretized problem with the expected order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07375 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary-value problems of functional differential equations with state-dependent delays andò, Alessia Sieber, Jan Numerical Analysis 65L03, 65L10, 65L20, 65L60 We prove convergence of piecewise polynomial collocation methods applied to periodic boundary value problems for functional differential equations with state-dependent delays. The state dependence of the delays leads to nonlinearities that are not locally Lipschitz continuous preventing the direct application of general abstract discretization theoretic frameworks. We employ a weaker form of differentiability, which we call mild differentiability, to prove that a locally unique solution of the functional differential equation is approximated by the solution of the discretized problem with the expected order. |
| title | Boundary-value problems of functional differential equations with state-dependent delays |
| topic | Numerical Analysis 65L03, 65L10, 65L20, 65L60 |
| url | https://arxiv.org/abs/2410.07375 |