title: Use of the Numerov method to improve the accuracy of the spatial discretisation in finite-difference electrochemical kinetic simulations.
abstract: 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.
authors.affiliation: Molten Salts Department, Institute of Physical Chemistry, Polish Academy of Sciences, Cracow. nbbienia@cyf-kr.edu.pl
authors.forename: L K
authors.initials: LK
authors.lastname: Bieniasz