Highly accurate, inexpensive procedures for computing chronoamperometric current, integral transformation kernel, and related integrals, for an inlaid disk electrode

Abstract

Recent theory of chronoamperometry at inlaid disk electrodes [L. K. Bieniasz, Electrochim. Acta 199 (2016) 1–11] provided a rigorous formula for the transient Faradaic current. However, numerical evaluation of the formula is costly and requires a multiprecision computing environment. In this work new procedures are developed for calculating the current and also the integral transformation kernel and related integrals needed by the adaptive Huber method for solving electrochemical Volterra integral equations. The procedures (implemented in C++) are computationally inexpensive (require less than a microsecond, of a contemporary processor time, per a single return value), but highly accurate (yield moduli of relative errors smaller than about 10−15 for the dimensionless time t¯≥0.01, and probably smaller than 10−13 for t¯<0.01). To achieve such a performance, new estimates of the coefficients of the small- t¯ asymptotic current expansion are deduced, the coefficients of the large- t¯ expansion are rederived with a high accuracy, and these expansions are combined with intermediate- t¯ polynomial approximations resulting from minimax fittings to reference data. The consistency of all these procedures is tested by simulating chronoamperometry by the adaptive Huber method. The procedures can be useful for simulation, testing/validating of diverse modelling techniques, and for experimental data analysis.