The Laplace Equation and other Steady-State Systems

Abstract

The Laplace equation comes into electrochemistry for the calculation of potential distributions around electrodes. These are not time-dependent phenomena on the sort of time scale we operate in; the propagation of a voltage field through an electrolyte is practically instantaneous. So we are looking here for steady-state solutions. The term “digital simulation” has somewhat of a dynamic flavour and does not apply so well to this problem area, which is in a class quite different from transport in electrolytes. The finite-difference method is useful here also, but takes on a quite different character. One of the striking differences is the amount of computer-time and -memory usually needed; tho other is the empirical bag of tricks workers use to speed things up.