We briefly review backward error analysis as a useful mathematical technique for improving
numerical methods used for solving ordinary differential equations describing dynamical
systems. Then, we show how backward error analysis-based compensation, an approach
recently introduced by the authors, can be applied to the second-order Newmark method
for eliminating numerical damping and achieving fourth-order convergence. The presented
improvements only require modifying the physical parameters of the system and the
excitation, while the Newmark method is left intact. We compare the performance of
the resulting improvements with that of several other numerical methods, including
a novel partitioned method based on local extrapolation.
