The application of fourth-order discretisations of the second derivative of concentration with respect to distance from the electrode, in electrochemical digital simulations, is examined. In the bulk of the diffusion space, a central five-point scheme is used, and six-point asymmetric schemes are used at the edges. In this paper, the scheme is applied to the BDF technique which allows higher orders in time as well. The method is found to be stable, using both the Neumann and matrix methods. Performance with BDF is not, however, optimal, levelling off at three-point BDF, as does the usual three-point approximation. This is shown to be due to startup problems inherent with BDF.