We propose and describe in detail an effective numerical algorithm for finding the stationary solution of charge transport problem in a DG-MOSFET. Hydrodynamical models describing the process of charge transport in semiconductors are sets of nonlinear PDE's with small parameters and specific conditions on the boundary of transistor that essentially complicates the process of numerical simulations. We construct a new algorithm based on the stabilization method and ideas of approximation without saturation and pseudo-spectral methods that enables one to overcome all of the mentioned difficulties. The proposed algorithm enables us to obtain the solution for different geometrical characteristics of DG-MOSFET and boundary conditions (including the non-symmetric cases) with extremely small values of dimensionless doping density and dielectric constant that are used in practice. (c) 2018 Elsevier Inc. All rights reserved.