Use of dynamically adaptive grid techniques for the solution of electrochemical kinetic equations: Part 16: Patch-adaptive strategy combined with the extended Numerov spatial discretisation

Electrochemical kinetic simulations by the patch-adaptive strategy outlined in the previous parts of this series of papers can be computationally expensive in the extreme cases of very thin boundary layers, moving fronts, or models defined over multiple spatial subintervals having disparate scales. The replacement of the second-order accurate conventional spatial discretisation (thus far used by the strategy) by the fourth-order accurate extended Numerov discretisation of Chawla [M.M. Chawla, J. Inst. Math. Appl. 22 (1978) 89], discussed in this work, allows one to reduce the computational costs. Numerical experiments with five representative examples of difficult-to-simulate kinetic models reveal that the reduction of the computational time, the number of spatial grid nodes needed, and spatial grid refinement levels, is particularly noticeable when a high spatial accuracy of the simulations is requested. At low accuracy demands the conventional spatial discretisation may be more efficient and more convenient to use. The patch-adaptive simulations by the extended Numerov scheme require spatial tolerance parameter TOLX values that are several times larger than the TOLX values that ensure a comparable accuracy by the conventional spatial discretisation.