THE VONNEUMANN STABILITY OF FINITE-DIFFERENCE ALGORITHMS FOR THE ELECTROCHEMICAL KINETIC SIMULATION OF DIFFUSION COUPLED WITH HOMOGENEOUS REACTIONS

The effect of kinetic terms for homogeneous reactions on the numerical stability of finite-difference algorithms for electrochemical kinetic simulations is examined theoretically using the von Neumann method. Stability criteria are presented for typical example kinetic equations in the case of the classic explicit, sequential explicit, second-order Runge-Kutta, Du Fort-Frankel, fully implicit, Crank-Nicolson and Saul'yev algorithms. The practical stability, related to the error growth for t --> infinity constant integration steps deltat and h, depends not only on the parameter lambda = D deltat/h2 but also on the rates of homogeneous reactions. In particular, the commonly used condition lambda less-than-or-equal-to 0.5 is insufficient for the stability of the classic explicit method when homogeneous kinetics are involved.