Multirate methods for ordinary differential equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910968791957504 |
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| author | Günther, Michael Sandu, Adrian |
| author_facet | Günther, Michael Sandu, Adrian |
| contents | This survey provides an overview of state-of-the art multirate schemes, which exploit the different time scales in the dynamics of a differential equation model by adapting the computational costs to different activity levels of the system. We start the discussion with the straightforward approach based on interpolating and extrapolating the slow--fast coupling variables; the multirate Euler scheme, used as a base example, falls into this class. Next we discuss higher order multirate schemes that generalize classical singlerate linear multistep, Runge-Kutta, and extrapolation methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_20062 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multirate methods for ordinary differential equations Günther, Michael Sandu, Adrian Numerical Analysis 65L05, 65L06, 65L07, 65L020 This survey provides an overview of state-of-the art multirate schemes, which exploit the different time scales in the dynamics of a differential equation model by adapting the computational costs to different activity levels of the system. We start the discussion with the straightforward approach based on interpolating and extrapolating the slow--fast coupling variables; the multirate Euler scheme, used as a base example, falls into this class. Next we discuss higher order multirate schemes that generalize classical singlerate linear multistep, Runge-Kutta, and extrapolation methods. |
| title | Multirate methods for ordinary differential equations |
| topic | Numerical Analysis 65L05, 65L06, 65L07, 65L020 |
| url | https://arxiv.org/abs/2505.20062 |