A variational symplectic scheme based on Simpson's quadrature
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914846959730688 |
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| author | Dubois, François Rojas-Quintero, Juan Antonio |
| author_facet | Dubois, François Rojas-Quintero, Juan Antonio |
| contents | We propose a variational symplectic numerical method for the time integration of dynamical systems issued from the least action principle. We assume a quadratic internal interpolation of the state and we approximate the action in a small time step by the Simpson's quadrature formula. The resulting scheme is explicited for an elementary harmonic oscillator. It is a stable, explicit, and symplectic scheme satisfying the conservation of an approximate energy. Numerical tests illustrate our theoretical study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16423 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A variational symplectic scheme based on Simpson's quadrature Dubois, François Rojas-Quintero, Juan Antonio Numerical Analysis We propose a variational symplectic numerical method for the time integration of dynamical systems issued from the least action principle. We assume a quadratic internal interpolation of the state and we approximate the action in a small time step by the Simpson's quadrature formula. The resulting scheme is explicited for an elementary harmonic oscillator. It is a stable, explicit, and symplectic scheme satisfying the conservation of an approximate energy. Numerical tests illustrate our theoretical study. |
| title | A variational symplectic scheme based on Simpson's quadrature |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2406.16423 |