High order spatial discretisations in electrochemical digital simulation. 2. Combination with the extrapolation algorithm

The application of fourth order discretisations of the second derivative of concentration with respect to distance from the electrode, in electrochemi cal digital simulations, is examined. In the bulk of the diffusion space, a central five-point scheme is used, and six-point asymmetric schemes are us ed at the edges. In this paper, the scheme is applied to the extrapolation technique, based on the backward implicit (BI) algorithm for temporal integ ration, which (with extrapolation) allows higher orders in time as well. Th e method is found to be stable, using both the von Neumann and matrix metho ds. Exceptional efficiency is obtained both for Cottrell and chronopotentio metry simulations, requiring as few as 3-5 steps in time, starting at the d imensionless time t = 0 to gain four-decimal accuracy at t = 1. (C) 2001 El sevier Science Ltd. All rights reserved.