Exploring Exponential Runge-Kutta Methods: A Survey
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908990388043776 |
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| author | andò, Alessia Cangiotti, Nicolò Sensi, Mattia |
| author_facet | andò, Alessia Cangiotti, Nicolò Sensi, Mattia |
| contents | In this survey, we provide an in-depth investigation of exponential Runge-Kutta methods for the numerical integration of initial-value problems. These methods offer a valuable synthesis between classical Runge-Kutta methods, introduced more than a century ago, and exponential integrators, which date back to the 1960s. This manuscript presents both a historical analysis of the development of these methods up to the present day and several examples aimed at making the topic accessible to a broad audience. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04024 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploring Exponential Runge-Kutta Methods: A Survey andò, Alessia Cangiotti, Nicolò Sensi, Mattia Numerical Analysis 65L03, 65L04, 65L05, 65L20, 65M12 In this survey, we provide an in-depth investigation of exponential Runge-Kutta methods for the numerical integration of initial-value problems. These methods offer a valuable synthesis between classical Runge-Kutta methods, introduced more than a century ago, and exponential integrators, which date back to the 1960s. This manuscript presents both a historical analysis of the development of these methods up to the present day and several examples aimed at making the topic accessible to a broad audience. |
| title | Exploring Exponential Runge-Kutta Methods: A Survey |
| topic | Numerical Analysis 65L03, 65L04, 65L05, 65L20, 65M12 |
| url | https://arxiv.org/abs/2507.04024 |