Symplectic integrators for second-order linear non-autonomous equations
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2017
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| Acceso en línea: | |
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| _version_ | 1866916212656570368 |
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| author | Bader, Philipp Blanes, Sergio Casas, Fernando Kopylov, Nikita Ponsoda, Enrique |
| author_facet | Bader, Philipp Blanes, Sergio Casas, Fernando Kopylov, Nikita Ponsoda, Enrique |
| contents | Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they differ in significant aspects. The first family is addressed to problems with low to moderate dimension, whereas the second is more appropriate when the dimension is large, in particular when the system corresponds to a linear wave equation previously discretised in space. Several numerical experiments illustrate the main features of the new schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1702_04768 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Symplectic integrators for second-order linear non-autonomous equations Bader, Philipp Blanes, Sergio Casas, Fernando Kopylov, Nikita Ponsoda, Enrique Numerical Analysis 65L07, 65L05, 65Z05 G.1.0 Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they differ in significant aspects. The first family is addressed to problems with low to moderate dimension, whereas the second is more appropriate when the dimension is large, in particular when the system corresponds to a linear wave equation previously discretised in space. Several numerical experiments illustrate the main features of the new schemes. |
| title | Symplectic integrators for second-order linear non-autonomous equations |
| topic | Numerical Analysis 65L07, 65L05, 65Z05 G.1.0 |
| url | https://arxiv.org/abs/1702.04768 |