Research concentrates on electrochemical digital simulation; that is, the solution of Fick's diffusion equation, with the special boundary conditions given by the electrochemical context. Some of the major problems have been solved, such as that of fast homogeneous reactions, coupled reactions, and stability in this context has been examined. We now have a handle on most of these problems and the publications list reflects activity on these fronts.

We have provided accurate reference values of the current at the ultramicrodisk and ultramicroband electrodes. Recent work includes simulation of the conical well electrode, the conical-tip electrode and accurate values of fluxes at cylindrical and capped cylindrical electrodes. An excursion outside electrochemistry dealt with the dynamics of thermal gas reactions; and within electrochemistry, more efficient ways of simulating enzyme systems. A more recent publication is on the optimisation of simulations of two-dimensional systems, comparing several transformations that have been suggested, investigating multi-point spatial derivative approximations, orthogonal collocation and the eigenvalue, -vector method. Some surprises were encountered in this work. Enzyme systems have been investigated, as were several ways to compute electric field effects, surface concentrations over a disk electrode, and the use of the Saul'yev method in two dimensions. There was another excursion into another field, simulating a system of chemical reactions in a biochemical context. Recently the behaviour of rectangular (including square) electrodes and arrays of square electrodes has been simulated, providing some steady state current values. In 2025, there was a collaboration of 15 authors on another biochemical paper, for which DB simulated te kinetics of a chain of reactions; the historical paper on the Sand equation and a Comment on a paper by Eswari and "kumar" [sic] by DB and Strutwolf.

External collaborators

Dr. Jörg Strutwolf

Institute for Print and Media Technology, Chemnitz University of Technology, 09107 Chemnitz, Germany

The collaboration is in digital simul ation, and has been ongoing since 2000.

Dr. Leslaw Bieniasz

Faculty of Electrical and Computer Engineering, Cracow University of Technology.

Since about 1993 there has been fruitful collaboration in the field of digital simulation, especially on issues of numerical stability. This work continues.

Full publication list