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An accurate simulation of charge transport in a charge-coupled device requires estimate to be made of fringing and self-induced fields. This has involved a two-dimensional solution for the potential distribution in the substrate, which can be expensive on computing time. The algorithm presented here restricts the calculation to a single set of nodal points along the surface of the device, and has been shown to be significantly faster, with little error, when compared with the corresponding two-dimensional solution. An attempt has also been made to obtain a simpler description of charge transport along the channel which avoids some of the problems which arise in the solution of the highly nonlinear transport equation. The simulation of two cases relevant to the operation of the CCD transfer process are presented. A study of injection from a source diffusion is also included.