LSV modelling of electrochemical systems through numerical inversion of Laplace transforms. I – The GS–LSV algorithm

Semi-analytical modelling of electrochemical reactions in the time domain generally requires prior knowledge of the inverse Laplace transform of the so-called mass-transfer function, MX(s) (with s being the variable of Laplace transform), which depends on the electrode geometry, the mass-transport process, the boundary conditions and the possible presence of coupled (homogeneous) chemical reactions. Oldham and co-workers have developed efficient convolution algorithms. Unfortunately, the semi-analytical approach becomes ineffective when the inverse transform of MX(s) cannot be derived analytically. Hence, a new approach of the dynamics of electrochemical systems is proposed in this work. The method is based on numerical inversion of Laplace transforms, and, more especially, on the Gaver–Stehfest inversion formula. The simple algorithm, proposed in this work, makes it possible to investigate a wide range of electrode geometry and chemical, electrochemical and one-dimensional mass-transport processes by potential-controlled techniques, and more especially linear scan and cyclic voltammetry (LSV and CV).