Automatic solution of integral equations describing electrochemical transients at dropping mercury electrodes

• Extension of the adaptive Huber method for electrochemical integral equations.
• It applies to integral equations for the expanding plane model of the DME.
• Solutions are obtained automatically with a prescribed accuracy.
• The method is tested on simple models of D.C. and A.C. polarography.

Polarographic experiments at dropping mercury electrodes belong to the classics of electroanalytical techniques. Theoretical modelling and computer simulation of such experiments is often based on the expanding plane model, which in the absence of homogeneous reactions is represented by one-dimensional convection–diffusion partial differential equations. The latter equations can be converted to integral equations involving a specific kernel function. In the present study, the adaptive Huber method, recently elaborated by the present author, has been extended to handle such a kernel function. The resulting simulation technique has been tested on examples of integral equations representing simple models of D.C. and A.C. polarography. The method is shown to provide automatic solutions, with a user-selected target accuracy. Errors corresponding to the range from about 10−2 of the maximum solution value, down to about 10−7 or even smaller, can be easily achieved at a modest computational cost.