Three different groups of explicit and unconditionally stable finite difference methods are described and used to simulate some electrochemical processes. These methods, which have not yet been used in electrochemistry, are the Du Fort-Frankel method, group explicit methods and Larkin's procedures. The straightforward use of the Saul'yev-RL algorithm, which belongs to the set of Larkin's procedures, was demonstrated to be one of the best alternatives yet available for this kind of calculation. In addition, the Du Fort-Frankel algorithm associated with an expanding space grid proved to be another attractive option for digital simulations.