  Haynes et al. (1977) derived a nonlinear differential equation to determine
the spread of innovations within a social network across space and time. This
model depends upon the imitators and the innovators within the social system,
where the imitators respond to internal influences, whilst the innovators react
to external factors. Here, this differential equation is applied to simulate
the uptake of a low-carbon technology (LCT) within a local electricity network
situated in the UK. This network comprises of many households that are assigned
to certain feeders. Firstly, travelling wave solutions of Haynes' model are
used to predict adoption times as a function of the imitation and innovation
influences. Then, the grid that represents the electricity network is created
so that the finite element method (FEM) can be implemented. Next, innovation
diffusion is modelled with Haynes' equation and the FEM, where varying
magnitudes of the internal and external pressures are imposed. Consequently,
the impact of these model parameters is examined. Moreover, LCT adoption
trajectories at fixed feeder locations are calculated, which give a macroscopic
understanding of the uptake behaviour at specific network sites. Lastly, the
adoption of LCTs at a household level is discussed.
