By Tom Holden and Michael Paetz
http://d.repec.org/n?u=RePEc:ham:qmwops:21207b&r=dge
This paper presents a fast, simple and intuitive algorithm for simulation of linear dynamic stochastic general equilibrium models with inequality constraints. The algorithm handles both the computation of impulse responses, and stochastic simulation, and can deal with arbitrarily many bounded variables. To illustrate the usefulness and efficiency of this algorithm we provide two applications according to the zero lower bound (ZLB) on nominal interest rates. Our solution principle is much faster than comparable methods. We therefore expect this algorithm to be very helpful also for estimation procedures, and for a wide range of applications apart from monetary policy analysis.
At least since some countries have been stuck at close to zero interest rates, inequality constraints have become an important issue in macroeconomics. Of course, model solutions based on linearization cannot take inequality conditions, and this paper shows a way around the issue that an in particular be implemented in DYNARE. But I remain unconvinced that this beats a higher order approximation.
NEP-DGE Blog 
You’re right that our method will never beat grid based methods in terms of accuracy. But what we can deliver is speed, even at scales for which grid based methods are not feasible even on super-computers.
Having said that, we will shortly be circulating a new version of the paper that extends our method to perturbation approximations of arbitrary order, and enables the method to be used alongside risky steady state solution methods. This enables fast approximations to the distortions caused by the risk of hitting the zero bound.