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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2405.04195 |
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| _version_ | 1866909348832215040 |
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| author | Arranz-Simón, Carlos Palencia, Cesar |
| author_facet | Arranz-Simón, Carlos Palencia, Cesar |
| contents | Starting from an A-stable rational approximation to $\rm{e}^z$ of order $p$, $$r(z)= 1+ z+ \cdots + z^p/ p! + O(z^{p+1}),$$ families of stable methods are proposed to time discretize abstract IVP's of the type $u'(t) = A u(t) + f(t)$. These numerical procedures turn out to be of order $p$, thus overcoming the order reduction phenomenon, and only one evaluation of $f$ per step is required. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04195 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rational methods for abstract linear, non-homogeneous problems without order reduction Arranz-Simón, Carlos Palencia, Cesar Numerical Analysis 65J10, 65M20, 65M12 Starting from an A-stable rational approximation to $\rm{e}^z$ of order $p$, $$r(z)= 1+ z+ \cdots + z^p/ p! + O(z^{p+1}),$$ families of stable methods are proposed to time discretize abstract IVP's of the type $u'(t) = A u(t) + f(t)$. These numerical procedures turn out to be of order $p$, thus overcoming the order reduction phenomenon, and only one evaluation of $f$ per step is required. |
| title | Rational methods for abstract linear, non-homogeneous problems without order reduction |
| topic | Numerical Analysis 65J10, 65M20, 65M12 |
| url | https://arxiv.org/abs/2405.04195 |