D-splitting methods: 2N -storage embedded explicit Runge-Kutta methods at any order using splitting methods
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911567317041152 |
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| author | Blanes, Sergio Escorihuela-Tomàs, Alejandro |
| author_facet | Blanes, Sergio Escorihuela-Tomàs, Alejandro |
| contents | Low-storage explicit Runge-Kutta schemes are particularly popular for the numerical integration of time-dependent partial differential equations based on the method-of-lines due to their efficiency and their reduced memory requirements. We show that D-splitting methods, splitting methods on the extended phase space, can be used as high performance 2N-storage embedded explicit RK methods without a third storage register. They are pseudo-geometric methods preserving some of the qualitative properties of the exact solution up to a higher order than the order of the method. Some of their properties are analysed, to build new tailored methods, and are tested on numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03457 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | D-splitting methods: 2N -storage embedded explicit Runge-Kutta methods at any order using splitting methods Blanes, Sergio Escorihuela-Tomàs, Alejandro Numerical Analysis Low-storage explicit Runge-Kutta schemes are particularly popular for the numerical integration of time-dependent partial differential equations based on the method-of-lines due to their efficiency and their reduced memory requirements. We show that D-splitting methods, splitting methods on the extended phase space, can be used as high performance 2N-storage embedded explicit RK methods without a third storage register. They are pseudo-geometric methods preserving some of the qualitative properties of the exact solution up to a higher order than the order of the method. Some of their properties are analysed, to build new tailored methods, and are tested on numerical examples. |
| title | D-splitting methods: 2N -storage embedded explicit Runge-Kutta methods at any order using splitting methods |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.03457 |