Singular transients in the presence of homogeneous reactions at cylindrical wire electrodes: Simulation by the adaptive Huber method for integral equations

Current transients possessing a weak temporal singularly of the t(-1/2) type arise in the theory of chronoamperometry and cyclic voltammetry. Simulating them by the method of integral equations (IEs) requires a highly accurate algorithm for computing integrals integral(t)(0) K (t, tau) tau(-1/2) d tau for any kernel term K(t, tau) present in the IEs. Such an algorithm is presented for the kernel term K(t, tau) = exp[-k(t - tau)]kcylw [p(t - tau)(1/2)] characteristic of IEs arising for diffusion coupled with (pseudo-) first order homogeneous reactions at cylindrical wire electrodes. The formerly described adaptive Huber method, equipped with this algorithm, is applied to three example IEs describing singular transients. These simulations are successful when the parameter k (typically a rate constant of a homogeneous reaction) and the electrode cylindricity parameter rho are moderately large. For too large k or rho a divergence of the method was observed, due to inevitable roundoff errors. Substantial amendments to the adaptive Huber method may be necessary in order to overcome this numerical difficulty.

Automated summary

This paper presents a high-precision algorithm for simulating singular transients in chronoamperometry and cyclic voltammetry. The algorithm is applied to integral equations with diffusion and (pseudo-)first order homogeneous reactions, and simulations are conducted for three example cases. The results are successful when the parameters are moderate, but a divergence is observed when the parameters are too large due to unavoidable roundoff errors.