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.
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Molten Salts Department, Institute of Physical Chemistry, Polish Academy of Sciences, Cracow. nbbienia@cyf-kr.edu.pl