The finite-difference patch-adaptive strategy for electrochemical kinetic simulations, introduced in Part 5 and extended in Part 10 of this series of papers, is further extended to time-dependent models involving migration-diffusion transport in one-dimensional space geometry. The extensions include: spatial discretisation of generalised second spatial derivative expressions typical of migration-diffusion equations: allowance for the dependence of boundary conditions on displacement current; support for an a posteriori calculation of the displacement current as one of the model responses; optional calculation of steady-state initial conditions;, the ability to use enhanced precision of floating point calculations. The extended strategy is used to simulate four examples of transient experiments, represented by Nernst-Planck-Poisson equation systems: coulostatic charge injection at ail ideally polarised planar electrode: a voltage step for a thin layer asymmetric electrochemical cell; chronopotentiometry for an electrolyte\membrane\electrolyte system; and chronopotentiometry for a bipolar membrane. The strategy provides fairly reliable solutions, but its automatism and efficiency are less satisfactory compared to models without electric migration, owing to the need for model-dependent tuning of the method parameters, and increased computational cost necessary for the exact adaptive determination of the electric potential profiles. (C) 2003 Elsevier B.V. All rights reserved.