The finite difference method of calculation of non-steady-state ion transfer in electrochemical systems under the conditions of natural convection is elaborated. The method is based on the mathematical model involving the continuity equations for electrolyte species, the condition of electroneutrality, and the Navier-Stokes equations for a viscous incompressible liquid with the corresponding initial and boundary conditions. A scheme of decoupling is proposed, which provides successive calculation of the field of hydrodynamic velocities (a stream function), the distribution of electric potential, and the distribution of electrolyte species concentrations subject to the condition of electroneutrality. To enhance the efficiency of the method at large Schmidt numbers, the distribution of electrolyte species concentrations was calculated by the implicit difference scheme. The results of computational experiments are reported. (C) 2003 Elsevier Science B.V. All rights reserved.