Automatic simulation of cyclic voltammograms by the adaptive Huber method for systems of weakly singular Volterra integral equations

Having in mind modern trends of laboratory automation in electroanalysis, and related efforts to create problem solving software for the modelling and simulation of electroanalytical experiments, the development and testing of diverse adaptive simulation methods is an important task. In former works of the present author an adaptive variant of the popular Huber method, serving for the solution of single integral equations pertinent to the theory of cyclic voltammetry, was proposed. The method has been recently extended to systems of second kind Volterra integral equations with weakly singular kernels and linear or non-linear dependences between the unknowns and their integrals. In the present work the validity of the extended method, for electrochemical simulations, is tested on representative examples of such integral equation systems, occurring in the theory of cyclic voltammetry. The performance of the adaptive simulations is found similar to the case of single integral equations, with the difference that the integral equation systems require a correspondingly larger computational cost compared to single integral equations.