  We discuss methods for numerically solving the generalized Master equation
GME which governs the time-evolution of the reduced density matrix of a
mechanically movable mesoscopic device in a dissipative environment. As a
specific example, we consider the quantum shuttle -- a generic quantum
nanoelectromechanical system (NEMS). When expressed in the oscillator basis,
the static limit of the GME becomes a large linear non-sparse matrix problem
(characteristic size larger than 10^4 by 10^4) which however, as we show, can
be treated using the Arnoldi iteration scheme. The numerical results are
interpreted with the help of Wigner functions, and we compute the current and
the noise in a few representative cases.
