Functional equivariance and modified vector fields
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866910974226726912 |
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| author | Stern, Ari Suri, Sanah |
| author_facet | Stern, Ari Suri, Sanah |
| contents | This paper examines functional equivariance, recently introduced by McLachlan and Stern [Found. Comput. Math. (2022)], from the perspective of backward error analysis. We characterize the evolution of certain classes of observables (especially affine and quadratic) by structure-preserving numerical integrators in terms of their modified vector fields. Several results on invariant preservation and symplecticity of modified vector fields are thereby generalized to describe the numerical evolution of non-invariant observables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01822 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Functional equivariance and modified vector fields Stern, Ari Suri, Sanah Numerical Analysis 37M15 This paper examines functional equivariance, recently introduced by McLachlan and Stern [Found. Comput. Math. (2022)], from the perspective of backward error analysis. We characterize the evolution of certain classes of observables (especially affine and quadratic) by structure-preserving numerical integrators in terms of their modified vector fields. Several results on invariant preservation and symplecticity of modified vector fields are thereby generalized to describe the numerical evolution of non-invariant observables. |
| title | Functional equivariance and modified vector fields |
| topic | Numerical Analysis 37M15 |
| url | https://arxiv.org/abs/2307.01822 |