A variational symplectic scheme based on Simpson's quadrature
Numerical Analysis
2024-06-25 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 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.
Keywords
Cite
@article{arxiv.2406.16423,
title = {A variational symplectic scheme based on Simpson's quadrature},
author = {François Dubois and Juan Antonio Rojas-Quintero},
journal= {arXiv preprint arXiv:2406.16423},
year = {2024}
}