  We study the time-bounded reachability problem for continuous-time Markov
decision processes (CTMDPs) and games (CTMGs). Existing techniques for this
problem use discretisation techniques to break time into discrete intervals,
and optimal control is approximated for each interval separately. Current
techniques provide an accuracy of O(\epsilon^2) on each interval, which leads
to an infeasibly large number of intervals. We propose a sequence of
approximations that achieve accuracies of O(\epsilon^3), O(\epsilon^4), and
O(\epsilon^5), that allow us to drastically reduce the number of intervals that
are considered. For CTMDPs, the performance of the resulting algorithms is
comparable to the heuristic approach given by Buckholz and Schulz, while also
being theoretically justified. All of our results generalise to CTMGs, where
our results yield the first practically implementable algorithms for this
problem. We also provide positional strategies for both players that achieve
similar error bounds.
