English

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.

Keywords

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

R2 v1 2026-06-28T17:20:58.460Z