Utility of super-time-stepping for electroanalytical digital simulations by explicit finite difference methods. Part 2: Spatially two- and three-dimensional models

The utility of super-time-stepping is examined, for digital simulations of selected electroanalytical experiments described by diffusion or reaction-diffusion partial differential equations in two- and three-dimensional space geometry. The tests focus on example models of chronoamperometry and cyclic voltammetry at inlaid band, disk and rectangle electrodes, assuming a single charge transfer or an EC' catalytic mechanism. The combination of the super-time-stepping with the classic explicit finite difference method is found to be distinctly more efficient (with speedups as large as 7) than the explicit method itself. Speedups obtained are also several times greater than in the case of one-dimensional simulations considered in Part 1. The method can be recommended for explicit two- and three-dimensional simulations, especially in conjunction with parallel implementations.