Simpson's quadrature for a nonlinear variational symplectic scheme
Numerical Analysis
2024-06-28 v1 Numerical Analysis
Abstract
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 between two time steps and we approximate the action in one time step by the Simpson's quadrature formula. The resulting scheme is nonlinear and symplectic. First numerical experiments concern a nonlinear pendulum and we have observed experimentally very good convergence properties.
Cite
@article{arxiv.2406.19000,
title = {Simpson's quadrature for a nonlinear variational symplectic scheme},
author = {François Dubois and Juan Antonio Rojas-Quintero},
journal= {arXiv preprint arXiv:2406.19000},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2406.16423