A highly accurate, inexpensive procedure for computing integral transformation kernel and its moment integrals for cylindrical wire electrodes

Abstract

Cylindrical wire or fiber electrodes are attractive for electro-analytical applications, but the theory of transient methods at such electrodes is complicated, necessitating approximate expressions or procedures for computing various special functions occurring in the theory. One of such functions is the integral transformation kernel function corresponding to semi-infinite pure diffusion conditions. In the present work a highly accurate and computationally inexpensive procedure for computing the cylindrical contribution to this kernel function is presented. The procedure relies on local polynomial approximations covering the entire argument domain, and it provides at least 14–15 significant digits. The procedure also computes qth order moment integrals of the kernel function (where q ⩾ 0 is a real number). The relative accuracy of 14–15 digits, of the moment integrals, has been verified for q = 0, 1 and 2. The procedure can be used in conjunction with numerical algorithms for the solution of integral equations or for the convolution analysis of experimental transients. It can also be used for the computation of chronopotentiometric responses to the programmed current density following the power-time dependence i( t) = i 0 t q with integer q ⩾ 0, which is shown as an example application.