Reference values of the chronoamperometric response at cylindrical and capped cylindrical electrodes

This work provides accurate solutions of the cylinder flux function I(0,1;T), first solved by Jaeger and Clarke, which can serve as reference values for electrochemical amperometric diffusion limited currents at a cylinder, as well as heat fluxes under equivalent conditions (fixed temperature at the cylinder surface). For the capped cylinder of varying lengths, reference values of time-dependent electrochemical currents are provided. Steady state currents at capped cylinders are presented and a function is provided that fits the simulated values to within 1%. All of these are more accurate than in previous works.     

Strategies for damping the oscillations of the alternating direction implicit method of simulation of diffusion-limited chronoamperometry at disk electrodes

Five methods are described for reducing or eliminating the error oscillations resulting from the application of the Peaceman-Rachford alternating direction implicit algorithm to disk electrode simulation problems involving an initial discontinuity, such as results from a potential jump at an electrode. The methods are: (a) the straight-forward application of the Peaceman-Rachford ADI algorithm, using sufficiently small time intervals so that the oscillations are damped at times for which accurate current values are needed; (b) using the first-order alternating direction implicit algorithm by Douglas and Rachford; (c) subdivision of the first simulation time interval into subintervals; (d) beginning the simulation with a few steps of the Douglas-Rachford algorithm followed by the Peaceman-Rachford method; and (e) presetting a reasonable approximation to the concentration profile at the end of the first simulation step and simulating from there on.Methods (d) and (e) are found clearly to be the most efficient at damping the oscillations, but method (b) also eliminates oscillations and leads to reasonable computation times, about one third of those needed for a sparse matrix solution of a two-dimensional system.     

A fourth-order accurate, three-point compact approximation of the boundary gradient, for electrochemical kinetic simulations by the extended Numerov method

The fourth-order accurate, three-point compact (extended Numerov) finite-difference scheme of Chawla [J. Inst. Math. Appl. 22 (1978) 89] has been recently found superior (in terms of accuracy and efficiency) to the conventional second-order accurate spatial discretisation commonly used in electrochemical kinetic simulations. However, the two-point compact boundary gradient approximation, accompanying the scheme, is difficult to apply in the case of time-dependent kinetic partial differential equations, because it introduces unwanted second temporal derivatives into calculations. The conventional five-point gradient formula is free from this drawback, but it is also not very convenient, owing to the locally increased bandwidth of the matrix of linear equations arising from the spatio-temporal discretisation. A new three-point compact boundary gradient approximation derived in this work, avoids the above inconveniences and economically re-uses expressions utilised by the extended Numerov discretisation. The fourth-order accuracy of the new approximation is proven theoretically and verified in computational experiments performed for examples of kinetic models.