The transmission-line modelling (t.l.m.) method presents a new approach to the solution of lumped networks by providing discrete models for components. Errors become due to the modelling process only and not due to the approximate solution of an approximate calculus model. The correspondence between stub models and existing implicit methods is shown and the concept of numerical parasitic components as a means of assessing errors is introduced. The paper then describes the entirely new explicit routines resulting from transmission-line modelling and explains their use in non-linear circuits. Finally, examples of mixed implicit and explicit working are given for the solution of non-linear transistor circuits.