Automatic simulation of electrochemical transients at cylindrical wire electrodes, by the adaptive Huber method for Volterra integral equations

Numerical solutions of integral equations describing controlled-potential transient experiments at cylindrical wire or fiber electrodes were rarely attempted in the past, seemingly due to the lack of adequate approximations to the kernel functions arising in such cases. In order to overcome this difficulty, in the former work of the present author a highly accurate approximation to the kernel function representing cylindrical diffusion in the absence of homogeneous reactions has been designed. In the present work the approximation is combined with the recently developed adaptive Huber method for solving electrochemical integral equations of Volterra type. The resulting method is tested on examples of kinetic models. The performance of the method is found similar to that previously reported for integral equations involving kernels specific for planar electrodes. The method provides automatic solutions with an accuracy that can be effectively set up by choosing an appropriate value of the error tolerance parameter. Errors corresponding to the range from about 10−2 (relative to the maximum solution value) down to about 10−6 or even less, can be easily achieved at a modest computational cost.