Automatic solution of integral equations pertinent to diffusion with first order homogeneous reactions at cylindrical wire electrodes

The application of the integral equation method to the modelling of controlled-potential transient experiments at cylindrical wire or fibre electrodes under conditions of diffusion coupled with (pseudo-) first order homogeneous reactions, was not attempted thus far. One of the reasons is the lack of simple closed-form formulae for the relevant integral transformation kernels. The algorithm presented in this work allows one to compute accurately (at least 13–15 significant digits) moment integrals of the kernel that most frequently occurs in such cases. It is assumed that the cylinder length to radius ratio is very large. The algorithm is combined with the recently developed adaptive Huber method for solving electrochemical integral equations. The resulting method is tested on example integral equations, including the equations of cyclic voltammetry for the catalytic mechanism, for which no former simulation reports have been available. The method provides automatic solutions with an accuracy that can be effectively achieved by choosing an appropriate value of the error tolerance parameter. Errors as small as 10−6 (relative to the maximum solution value) or even smaller, are obtainable, at a moderate computational cost. In this way, a variety of integral equations pertinent to cylindrical wire electrodes can now be solved easily and reliably.