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 electroc hemical kinetics. The discretization of such boundary conditions, curr ently used in connection with the Crank-Nicolson finite difference sol ution algorithm, is based on the forward difference gradient approxima tion, and may in some cases become numerically unstable. Therefore, we analyse the numerical stability of a number of alternative discretiza tions that have not yet been used in electrochemical simulations. The discretizations are based on the forward, central and backward differe nce gradient approximations. We show that some variants of the central and backward difference gradient approximations ensure the unconditio nal stability of the Crank-Nicolson method and can, therefore, be of p ractical interest. Furthermore, we show that the discretization used s o far is the least susceptible to error oscillations in time. Copyrigh t (C) 1998 Elsevier Science Ltd.