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

Abstract

Current transients possessing a weak temporal singularity 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 ∫0tK(t,τ)τ-1/2dτ for any kernel term K(t,τ) present in the IEs. Such an algorithm is presented for the kernel term K(t,τ)=exp[-k(t-τ)]kcylw[ρ(t-τ)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 ρ are moderately large. For too large k or ρ 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.