A FAST QUASI-EXPLICIT FINITE-DIFFERENCE METHOD FOR SIMULATING ELECTROCHEMICAL PHENOMENA .1. APPLICATION TO CYCLIC VOLTAMMETRIC PROBLEMS

A fast quasi-explicit finite difference (FQEFD) method is developed for the simulation of cyclic voltammetry of electrochemical systems comprising coupled heterogeneous and homogeneous kinetics. The heart of the present approach is the DuFort-Frankel algorithm. The simplicity of formulation of code usually associated with explicit finite difference (EFD) methods is retained. The FQEFD approach is particularly effective for dealing with stiff problems which involve very large values of one or more homogeneous rate constants. For certain problems the enhancement in computational speed of the FQEFD method relative to the EFD method can be many orders of magnitude. The accuracy of the method is demonstrated by simulations of cyclic voltammetry of a simple electron transfer, A+e- ⇌ B, and of a simple electron transfer coupled with a following quasi-reversible first-order homogeneous chemical reaction, B ⇌ C, or with a following quasi-reversible second-order homogeneous chemical reaction, 2B ⇌ C. Simulation results are compared to known, accepted solutions. Quick-Basic programs were executed on an IBM PS2-70 with an 80387 coprocessor, a level of computational power that is adequate for simulating many problems of interest. © 1990.