A numerical solution of the Nernst-Planck-Poisson (NPP) problem is presented in the paper. The driving forces are the concentration gradients and the electric field. The NPP equations are discretized in space and time and the resulting set of difference equations is solved numerically using the Rosenbrock method in Mathcad 12. The NPP model is used for simulations of transient potential responses to a step current perturbation. This allows for determining impedance spectra of nano- and meso-scale films (L= 10^-8, 10^-7 or 10^-6 m) contacted with permselective electrodes (blocking for anions). Simulated complex impedances exhibit different features depending on interface kinetics. The Warburg type spectrum has been obtained only for L= 10^-6 m and relatively high interfacial kinetics. The present numerical method allows for the direct relating between transport properties of the bulk and the interfaces (ionic diffusivities and heterogeneous rate constants) and complex impedances of electrochemical systems. [DOI: 10.1380/ejssnt.2006.464]