The effect of the discretization of the mixed boundary conditions on the numerical stability of the Crank-Nicolson algorithm of electrochemical kinetic simulations

Mixed boundary conditions with time-dependent coefficients are typical for diffusional initial boundary value problems occurring in electrochemical kinetics. The discretization of such boundary conditions, currently used in connection with the Crank-Nicolson finite difference solution algorithm, is based on the forward difference gradient approximation, and may in some cases become numerically unstable. Therefore, we analyse the numerical stability of a number of alternative discretizations that have not yet been used in electrochemical simulations. The discretizations are based on the forward, central and backward difference gradient approximations. We show that some variants of the central and backward difference gradient approximations ensure the unconditional stability of the Crank-Nicolson method and can, therefore, be of practical interest. Furthermore, we show that the discretization used so far is the least susceptible to error oscillations in time. Copyright (C) 1998 Elsevier Science Ltd.