The network thermodynamics approach has been used to obtain the numerical solutions of the Nernst-Planck and Poisson equations governing the ionic transport in electrochemical cells, including electrical double-layer (EDL) effects. By using the electric circuit simulation program PSPICE, a model has been proposed, which permits easily the numerical solutions of those equations describing the behavior of the system under steady-state and equilibrium conditions, as well as the transient and frequency responses to electrical perturbations. Two physical problems are studied, namely, (i) the formation of the equilibrium EDL and (ii) the transient and frequency responses of the system to electric potential perturbations. Impedance-frequency responses and the time evolution of the surface charge density on the electrodes and the electric current density are given. Also, the ionic concentration, the electric potential and the electric field profiles across the cell were obtained as a function of time. The method is quite general and extremely efficient and permits dealing with multiion systems, whatever the boundary and experimental conditions may be.