  We present the first review of methods to overapproximate the set of
reachable states of linear time-invariant systems subject to uncertain initial
states and input signals for short time horizons. These methods are fundamental
to state-of-the-art reachability algorithms for long time horizons, which
proceed in two steps: First they use such a method to discretize the system for
a short time horizon, and then they efficiently obtain a solution of the new
discrete system for the long time horizon. Traditionally, both qualitative and
quantitative comparison between different reachability algorithms has only
considered the combination of both steps. In this paper we study the first step
in isolation. We perform a variety of numerical experiments for six fundamental
discretization methods from the literature. As we show, these methods have
different trade-offs regarding accuracy and computational cost and, depending
on the characteristics of the system, some methods may be preferred over
others. We also discuss preprocessing steps to improve the results and
efficient implementation strategies.
