In order to investigate the stability of both equilibria
and periodic orbits of linear delayed dynamical systems
we employ the numericalmethod recently proposed by
the authors for discretizing the associated evolution family.
The objective is the efficient computation of stability charts
for varying or uncertain system parameters. A benchmark
set of tests is provided including computational data such as
the accuracy of the stability boundaries and the total computational
time, with particular reference to the delayed Mathieu
equation.