A variational symplectic scheme based on Lobatto's quadrature
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912674533605376 |
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| author | Dubois, François Rojas-Quintero, Juan Antonio |
| author_facet | Dubois, François Rojas-Quintero, Juan Antonio |
| contents | We present a variational integrator based on the Lobatto quadrature for the time integration of dynamical systems issued from the least action principle. This numerical method uses a cubic interpolation of the states and the action is approximated at each time step by Lobatto's formula. Numerical analysis is performed on both a harmonic oscillator and a nonlinear pendulum. The geometric scheme is conditionally stable, sixth-order accurate, and symplectic. It preserves an approximate energy quantity. Simulation results illustrate the performance and the superconvergence of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A variational symplectic scheme based on Lobatto's quadrature Dubois, François Rojas-Quintero, Juan Antonio Numerical Analysis We present a variational integrator based on the Lobatto quadrature for the time integration of dynamical systems issued from the least action principle. This numerical method uses a cubic interpolation of the states and the action is approximated at each time step by Lobatto's formula. Numerical analysis is performed on both a harmonic oscillator and a nonlinear pendulum. The geometric scheme is conditionally stable, sixth-order accurate, and symplectic. It preserves an approximate energy quantity. Simulation results illustrate the performance and the superconvergence of the proposed method. |
| title | A variational symplectic scheme based on Lobatto's quadrature |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.00560 |