Automatic solution of the Singh and Dutt integral equations for channel or tubular electrodes, by the adaptive Huber method

Abstract

Digital simulation of transient experiments at channel and tubular electrodes can be performed approximately but relatively cheaply, by means of the integral equation based approach introduced by Singh and Dutt [J. Electroanal. Chem. 182 (1985) 259]. Unfortunately, the use of the series expansion for the relevant integral transformation kernel, suggested by Singh and Dutt, makes such calculations overly slow. A new series expansion is proposed in the present study, which, when combined with the former expansion, yields inexpensive approximations to the kernel and its moment integrals. The relative error of these approximations is at the level of 10−16. The approximations are incorporated into the adaptive Huber method, developed by the present author. The method is shown to provide automatic solutions to the representative integral equations describing chronoamperometry for irreversible charge transfer and cyclic voltammetry for irreversible and reversible charge transfer. Desired accuracy of the solutions is selected simply by specifying a value of the error tolerance parameter. Errors corresponding to the range from about 10−2 of the maximum solution value, down to about 10−7 or even smaller, can be easily obtained at a modest computational cost.