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| Autori principali: | , , |
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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2510.15481 |
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| _version_ | 1866918162528731136 |
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| author | Arranz-Simón, Carlos Cano, Begoña Palencia, César |
| author_facet | Arranz-Simón, Carlos Cano, Begoña Palencia, César |
| contents | Given an $A$-stable rational approximation to $e^z$ of order $p$, numerical procedures are suggested to time integrate abstract, well-posed IBVPs, with time-dependent source term $f$ and boundary value $g$. These procedures exhibit the optimal order $p$ and can be implemented by using just one single evaluation of $f$ and $g$ per step, i.e., no evaluations of the derivatives of data are needed, and are of practical use at least for $p\le 6$. The full discretization is also studied and the theoretical results are corroborated by numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15481 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rational methods for abstract linear initial boundary value problems without order reduction Arranz-Simón, Carlos Cano, Begoña Palencia, César Numerical Analysis 65J10, 65M15 Given an $A$-stable rational approximation to $e^z$ of order $p$, numerical procedures are suggested to time integrate abstract, well-posed IBVPs, with time-dependent source term $f$ and boundary value $g$. These procedures exhibit the optimal order $p$ and can be implemented by using just one single evaluation of $f$ and $g$ per step, i.e., no evaluations of the derivatives of data are needed, and are of practical use at least for $p\le 6$. The full discretization is also studied and the theoretical results are corroborated by numerical experiments. |
| title | Rational methods for abstract linear initial boundary value problems without order reduction |
| topic | Numerical Analysis 65J10, 65M15 |
| url | https://arxiv.org/abs/2510.15481 |