In the first paper in this series we derived an exponentially expanding mesh designed specifically to give a fast, efficient solution to the problem of simulation of diffusion processes at microdisc electrodes to a pre-determined level of accuracy. In this paper we make use of this mesh to consider the problem of linear sweep voltammetry and show that for the simulated values of the peak current for a fully reversible reaction we can obtain agreement with previous analytic results to within 0.25% at all parameter values of interest. We go on to consider irreversible and quasi-reversible systems, and demonstrate good qualitative agreement with previously described numerical and analytical results. We again make use of the FIRM and the ADI finite difference methods, and discuss when each of these methods is most appropriate.