We use backward error analysis for differential equations to obtain modified or distorted equations describing the behaviour of the Newmark scheme applied to the transient structural dynamics equation. Using these results, we show how to construct compensation terms from the original parameters of the system, which improve the performance of Newmark simulations without changing the time step or modifying the scheme itself. Two such compensations are given: one eliminates numerical damping, while the other achieves fourth-order accurate calculations using the traditionally second-order Newmark method.

翻译：我们采用微分方程的后向误差分析方法，推导出描述Newmark格式应用于瞬态结构动力学方程时行为的修正方程（即畸变方程）。基于这些结果，我们展示了如何从系统原始参数构建补偿项，在不改变时间步长或修改格式本身的前提下提升Newmark仿真性能。给出了两种补偿方案：一种消除数值阻尼，另一种使传统二阶精度的Newmark方法实现四阶精度计算。