A FAST IMPLICIT FINITE-DIFFERENCE ALGORITHM FOR THE DIGITAL-SIMULATION OF ELECTROCHEMICAL PROCESSES

A fast implicit finite difference (FIFD) method arises from the combination of the exponentially expanding space model with an implicit simulation algorithm. Because of its unconditional stability, the algorithm can handle homogeneous and heterogeneous rate constants of any order of magnitude with potential steps of several millivolts. The treatment of those mechanisms, comprising homogeneous first- or second-order reactions, by means of the FIFD model leads to uniform matrix equations which can be solved effectively. The computation time for complex mechanisms with myriad kinetic couplings increases proportionally to m3 (n + 1) where m is the number of species involved and n denotes the number of space boxes required.