Improving the accuracy of the spatial discretization in finite-difference electrochemical kinetic simulations, by means of the extended Numerov method

The fourth-order accurate, three-point finite-difference Numerov spatial discretization provides accurate and efficient solutions to the time-dependent governing differential equations of electrochemical kinetics in one-dimensional space geometry, when the equations contain first time derivatives of the solution, second spatial derivatives, and homogeneous reaction terms only. However, the original Numerov discretization is not applicable when the governing equations involve first spatial derivative terms. To overcome this limitation, an appropriately extended Numerov discretization is required. We examine the utility of one of such extensions, first described by Chawla. Relevant discrete formulae are outlined for systems of linear governing equations involving first derivative terms, and applied to five representative example models of electrochemical transient experiments. The extended Numerov discretization proves to have an accuracy and efficiency comparable to the original Numerov scheme, and its accuracy is typically up to four orders of magnitude higher, compared to the conventional, second-order accurate spatial discretization, commonly used in electrochemistry. This results in a considerable improvement of efficiency. Therefore, the application of the extended Numerov discretization to the electrochemical kinetic simulations can be fully recommended.