The five-level Richtmyer modification of the fully implicit Laasonen finite difference algorithm is shown to exhibit superb accuracy and rapid convergence for the simulation of electrochemical phenomena, supporting the very wide range of values of the dimensionaless diffusion parameter D* (D* = DDELTAt/DELTAx2) from 10 to 10(20). Large values of D* are essential for accurate and efficient simulations of systems involving a wide dynamic range of homogeneous kinetic rates. The performance is tested by simulations of Cottrellian diffusion and executed using a minor modification of Rudolph’s fast implicit finite difference algorithm. The accuracy of the simulations is verified by comparing simulated values of time-dependent fluxes and flux integrals and time- and distance-dependent concentrations, with values computed from known analytic solutions.