High-order Gauss-Legendre methods admit a composition representation and a conjugate-symplectic counterpart
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915596167282688 |
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| author | Iavernaro, Felice Mazzia, Francesca Hairer, Ernst |
| author_facet | Iavernaro, Felice Mazzia, Francesca Hairer, Ernst |
| contents | One of the most classical pairs of symplectic and conjugate-symplectic schemes is given by the Midpoint method (the Gauss-Runge-Kutta method of order 2) and the Trapezoidal rule. These can be interpreted as compositions of the Implicit and Explicit Euler methods, taken in direct and reverse order, respectively. This naturally raises the question of whether a similar composition structure exists for higher-order Gauss-Legendre methods. In this paper, we provide a positive answer by first examining the fourth-order case and then outlining a generalization to higher orders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16809 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-order Gauss-Legendre methods admit a composition representation and a conjugate-symplectic counterpart Iavernaro, Felice Mazzia, Francesca Hairer, Ernst Numerical Analysis 65L06 G.1.7 One of the most classical pairs of symplectic and conjugate-symplectic schemes is given by the Midpoint method (the Gauss-Runge-Kutta method of order 2) and the Trapezoidal rule. These can be interpreted as compositions of the Implicit and Explicit Euler methods, taken in direct and reverse order, respectively. This naturally raises the question of whether a similar composition structure exists for higher-order Gauss-Legendre methods. In this paper, we provide a positive answer by first examining the fourth-order case and then outlining a generalization to higher orders. |
| title | High-order Gauss-Legendre methods admit a composition representation and a conjugate-symplectic counterpart |
| topic | Numerical Analysis 65L06 G.1.7 |
| url | https://arxiv.org/abs/2506.16809 |