A variational symplectic scheme based on Lobatto's quadrature
Numerical Analysis
2025-10-30 v3 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2504.00560,
title = {A variational symplectic scheme based on Lobatto's quadrature},
author = {François Dubois and Juan Antonio Rojas-Quintero},
journal= {arXiv preprint arXiv:2504.00560},
year = {2025}
}