NUMERICAL STABILITY OF FINITE-DIFFERENCE ALGORITHMS FOR ELECTROCHEMICAL KINETIC SIMULATIONS - MATRIX STABILITY ANALYSIS OF THE CLASSIC EXPLICIT, FULLY IMPLICIT AND CRANK-NICOLSON METHODS AND TYPICAL PROBLEMS INVOLVING MIXED BOUNDARY-CONDITIONS

The stepwise numerical stability of the classic explicit, fully implic it and Crank-Nicolson finite difference discretizations of example dif fusional initial boundary value problems from electrochemical kinetics has been investigated using the matrix method of stability analysis. Special attention has been paid to the effect of the discretization of the mixed, linear boundary condition with time-dependent coefficients on stability, assuming the two-point forward-difference approximation s for the gradient at the left boundary (electrode). Under accepted as sumptions one obtains the usual stability criteria for the classic exp licit and fully implicit methods. The Crank-Nicolson method turns out to be only conditionally stable in contrast to the current thought reg arding this method.