A singularity correction procedure for digital simulation of potential-step chronoamperometric transients in one-dimensional homogeneous reaction–diffusion systems

Transient solutions for potential-step chronoamperometry, obtained by conventional finite-difference simulations, are usually grossly inaccurate in the neighbourhood of temporal discontinuities in boundary conditions. In the case of one-dimensional homogeneous reaction–diffusion systems this problem can be overcome by applying a singularity correction procedure proposed in this work. The procedure is a modification of the approach recently suggested by Flyer and Fornberg [J. Comput. Phys. 184 (2003) 526] for the solution of partial differential equations with incompatible initial/boundary conditions. It consists of decomposing any concentration profile into a sum of two components: an analytically obtainable one that satisfies discontinuous boundary conditions but ignores homogeneous reaction(s), and a numerically obtainable part that satisfies continuous boundary conditions and takes the homogeneous reactions into account. A similar decomposition can also be applied to the electric current. Computational tests performed for four simple examples of electrochemical systems indicate that the most accurate results (close to the discontinuity) are obtained by combining the decomposition of the concentrations, applied at all discrete time levels, with the decomposition of the current.