Energy-preserving continuous-stage partitioned Runge-Kutta methods
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866915406842691584 |
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| author | Tang, Wensheng |
| author_facet | Tang, Wensheng |
| contents | In this paper, we present continuous-stage partitioned Runge-Kutta (csPRK) methods for energy-preserving integration of Hamiltonian systems. A sufficient condition for the energy preservation of the csPRK methods is derived. It is shown that the presented condition contains the existing condition for energy-preserving continuous-stage Runge-Kutta methods as a special case. A noticeable and interesting result is that when we use the simplifying assumptions of order conditions and the normalized shifted Legendre polynomials for constructing high-order energy-preserving csPRK methods, both the Butcher "weight" coefficients $B_τ$ and $\widehat{B}_τ$ must be equal to $1$. As illustrative examples, new energy-preserving integrators are acquired by virtue of the presented condition, and for the sake of verifying our theoretical results, some numerical experiments are reported. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_02391 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Energy-preserving continuous-stage partitioned Runge-Kutta methods Tang, Wensheng Numerical Analysis In this paper, we present continuous-stage partitioned Runge-Kutta (csPRK) methods for energy-preserving integration of Hamiltonian systems. A sufficient condition for the energy preservation of the csPRK methods is derived. It is shown that the presented condition contains the existing condition for energy-preserving continuous-stage Runge-Kutta methods as a special case. A noticeable and interesting result is that when we use the simplifying assumptions of order conditions and the normalized shifted Legendre polynomials for constructing high-order energy-preserving csPRK methods, both the Butcher "weight" coefficients $B_τ$ and $\widehat{B}_τ$ must be equal to $1$. As illustrative examples, new energy-preserving integrators are acquired by virtue of the presented condition, and for the sake of verifying our theoretical results, some numerical experiments are reported. |
| title | Energy-preserving continuous-stage partitioned Runge-Kutta methods |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1808.02391 |