  We present a new and improved method for simultaneous control of temperature
and pressure in molecular dynamics simulations with periodic boundary
conditions. The thermostat-barostat equations are build on our previously
developed stochastic thermostat, which has been shown to provide correct
statistical configurational sampling for any time step that yields stable
trajectories. Here, we extend the method and develop a set of discrete-time
equations of motion for both particle dynamics and system volume in order to
seek pressure control that is insensitive to the choice of the numerical time
step. The resulting method is simple, practical, and efficient. The method is
demonstrated through direct numerical simulations of two characteristic model
systems - a one dimensional particle chain for which exact statistical results
can be obtained and used as benchmarks, and a three dimensional system of
Lennard-Jones interacting particles simulated in both solid and liquid phases.
The results, which are compared against the method of Kolb & Dunweg, show that
the new method behaves according to the objective, namely that acquired
statistical averages and fluctuations of configurational measures are accurate
and robust against the chosen time step applied to the simulation.
