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.

翻译：我们提出了一种变分辛数值方法，用于对源自最小作用量原理的动力系统进行时间积分。我们假设状态在两个时间步之间具有二次内部插值，并使用辛普森求积公式近似单个时间步内的作用量。所得格式是非线性且保辛的。初步数值实验针对非线性单摆进行，我们通过实验观测到该方法具有极佳的收敛特性。