Automatic simulation of electrochemical transients by the adaptive Huber method for Volterra integral equations involving Kernel terms exp[−α(t − τ)]erex{[β(t − τ)]^1/2} and exp[−α(t − τ)]daw {[β(t − τ)]^1/2}

Abstract

Development of fully automatic methods for the simulation of transient experiments in electroanalytical chemistry is a desirable element of the contemporary trends of laboratory automation in electrochemistry. In accord with this idea, the adaptive Huber method, elaborated by the present author, is intended to solve automatically integral equations of Volterra type, encountered in the theory of controlled-potential transients. The coefficients of the method have been recently obtained for integral transformation kernels involving terms K(t, τ) = exp[−α(t − τ)]erex{[β(t − τ)]^1/2} and K(t, τ) = exp[−α(t − τ)]daw{[β(t − τ)]^1/2} with α ≥ 0 and β ≥ 0, which are known to occur in the above integral equations. In this work the validity of the resulting method, for electrochemical simulations, is examined using representative examples of electroanalytical models involving integral equations with various special cases of such kernel terms. The performance of the method is found similar to that previously reported for integral equations involving exclusively kernels K(t, τ) = 1, K(t, τ) = (t − τ)^−1/2, and K(t, τ) = exp[−λ (t − τ)](t − τ)^−1/2 with λ > 0.