  We present further developments of the auxiliary master equation approach
(AMEA), a numerical method to simulate many-body quantum systems in as well as
out of equilibrium, and apply it to the Interacting Resonant Level Model (IRLM)
to benchmark the new developments. In particular, our results are obtained by
employing the stochastic wave functions (SWF) method to solve the auxiliary
open quantum system arising within AMEA. This development allows to reach
extremely low wall-times for the calculation of correlation functions with
respect to previous implementations of AMEA. An additional significant
improvement is obtained by extrapolating a series of results obtained by
increasing the number of auxiliary bath sites, $N_B$, used within the auxiliary
open quantum system formally to the limit of $ N_B \rightarrow \infty$. Results
for the current-voltage characteristics and for equilibrium correlation
functions are compared with the one obtained by exact and matrix-product based
approaches.
