标题： 基于Lobatto求积的变分辛格式 显示英文标题

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

摘要： 我们提出了一种基于Lobatto求积的时间积分变分积分器，用于源自最小作用量原理的动力学系统的数值模拟。 该数值方法使用状态的三次插值，并通过Lobatto公式在每个时间步近似作用量。 针对谐振子进行了数值分析。 该格式条件稳定，具有六阶精度且辛。 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。 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 a harmonic oscillator. The scheme is conditionally stable, sixth-order accurate, and symplectic. It preserves an approximate energy quantity. Simulation results illustrate the performance of the proposed method.