  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.
