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 extrapolation technique, based on the backward implicit (BI) algorithm for temporal integration, which (with extrapolation) allows higher orders in time as well. The method is found to be stable, using both the von Neumann and matrix methods. Exceptional efficiency is obtained both for Cottrell and chronopotentiometry simulations, requiring as few as 3-5 steps in time, starting at the dimensionless time t = 0 to gain four-decimal accuracy at t = 1.