AN EFFICIENT NUMERICAL-METHOD OF SOLVING THE ABEL INTEGRAL-EQUATION FOR CYCLIC VOLTAMMETRY

An efficient, apparently numerically stable and sufficiently accurate algorithm of solving the Abel integral equation for cyclic voltammetry has been proposed. The method is analogous to that of replacing the kernel of a Fredholm integral equation by a degenerate one. An approximate expression for the kernel (zeta - z)-1/2 has been suggested which allows the determination of current function values in the range zeta is-an-element-of [0.001 55, 30.] of the non-dimensional time parameter zeta. Depending on the number of integration steps, the algorithm can be faster by 1-3 orders of magnitude than the traditional Huber method. The memory requirements are also much lower. The method can be extended to other cyclic voltammetric integral equations involving (zeta - z)-1/2 kernels. A similar approach can be used for an approximate semi-integration, enabling e.g. a fast global analysis of cyclic voltammograms.