Five methods are described for reducing or eliminating the error oscillations resulting from the application of the Peaceman-Rachford alternating direction implicit algorithm to disk electrode simulation problems involving an initial discontinuity, such as results froth a potential jump at an electrode. The methods are: (a) the straight-forward application of the Peaceman-Rachford ADI algorithm, using sufficiently small time intervals so that the oscillations are damped at times for which accurate current values are needed; (b) using the first-order alternating direction implicit algorithm by Douglas and Rachford; (c) subdivision of the first simulation time interval into subintervals; (d) beginning the simulation with a few steps of the Douglas-Rachford algorithm followed by the Peaceman-Rachford method; and (e) presetting a reasonable approximation to the concentration profile at the end of the first simulation step and simulating from there on. Methods (d) and (e) are found clearly to be the most efficient at damping the oscillations but method (b) also eliminates oscillations and leads to reasonable computation times, about one third of those needed for a sparse matrix solution of a two-dimensional system. (C) 2009 Elsevier B.V. All rights reserved.