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

Considering modern trends of laboratory automation in electroanalysis, the development of adaptive methods for automatic simulation of electrochemical transient techniques such as cyclic voltammetry is a topical issue. One of the classical simulation approaches relies on formulating, and solving numerically, relevant integral equations. In former work of the present author an adaptive variant of the popular Huber method serving for this purpose has been proposed, and successfully tested on electrochemical examples of first kind Abel integral equations (IEs). The method has been recently extended to second kind Volterra integral equations with weakly singular kernels and linear and 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 equations, occurring in the theory of cyclic voltammetry. The performance of the method is found satisfactory, although errors of the simulated transients may deviate from the prescribed error tolerance parameter, so that achieving a given target accuracy is less straightforward than it was for the voltammograms described by the first kind Abel equations.