Use of the Numerov method to improve the accuracy of the spatial discretisation in finite-difference electrochemical kinetic simulations

The fourth order accuracy of the spatial discretisation of time-dependent reaction–diffusion equations, in finite-difference electrochemical kinetic simulations in one space dimension, might well be achieved by means of the three-point Numerov method, instead of the 5(6)-point discretisation of second spatial derivatives, recently suggested in the literature. This is proven theoretically, and tested in simulations of potential-step chronoamperometric and current-step chronopotentiometric transients for the Reinert–Berg system, which is a classical example of electrochemical reaction–diffusion equations. Although less generally applicable than the 5(6)-point spatial scheme, the Numerov discretisation is easier to use, because it does not lead to increased linear equation matrix bandwidth, but results in quasi-block-tridiagonal matrices, similar to those for the conventional, second order accurate, three-point spatial discretisation. The simulations reveal that the Numerov method brings an improvement of accuracy and efficiency that is comparable with the one offered by the 5(6)-point spatial scheme.