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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. [GSI 2025, 26 June 2025.]

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A Variational Symplectic Scheme Based on Lobatto’s Quadrature

  • 会议论文

  • 发表日期：

    2026年

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  • François Dubois,
  • Juan Antonio Rojas-Quintero

摘要

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. [GSI 2025, 26 June 2025.]