标题： 基于Lobatto求积的变分辛算法 显示英文标题

标题： A variational symplectic scheme based on Lobatto's quadrature

摘要： 我们提出一种基于Lobatto求积的变分积分器，用于从最小作用量原理得出的动力系统的时域积分。 该数值方法使用状态的三次插值，且在每个时间步长上通过Lobatto公式近似作用量。 数值分析分别针对简谐振子和非线性摆进行。 几何方案是条件稳定的，六阶精度的，并且是辛的。 它保持一个近似的能量量。 仿真结果展示了所提出方法的性能和超收敛性。 显示英文摘要

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.