The finite-difference patch-adaptive strategy (PAS) for electrochemical kinetic simulations, previously described by the author, is extended and applied to two examples of non-linear diffusion in one-dimensional space geometry, characterised by moving fronts, and related to the modelling of redox switching of conductive polymers. The extension consists of an appropriate spatial discretisation of the second derivative diffusion term involving concentration-dependent diffusion coefficient, and of an improved selection of starting approximations for the Newton iterations within the extrapolation time-stepping scheme. Adaptive solutions obtained are reliable, accurate, efficient, and superior to fixed-grid solutions.