Improving the accuracy of the Newmark method through backward error analysis

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.