We describe the method of achieving the first completely general simulation of ac linear sweep and cyclic voltammetry making use of the Fully implicit Richtmyer modification (FIRM) method. The simulation technique is applied to a reversible process under conditions where a sinusoidal waveform of any amplitude is superimposed onto the de potential which is swept at a finite scan rate. Results, where possible, are compared with the existing theory derived at constant de potential to confirm the fidelity of the simulation. In particular, we demonstrate excellent agreement with the results of Engblom et al. [J. Electroanal. Chem. xxx (1999) xxx] for large amplitude ac voltammetry described in the companion paper immediately preceding this article. The use of conventional and Fourier transform methods of data analysis are compared to highlight the advantages of the use of the fast Fourier transform algorithm in ac voltammetry.