The presence of a large pinch velocity in the edge pedestal of high-confinement (H-mode) tokamak plasmas implies that particle transport in the plasma edge must be treated by a generalized pinch-diffusion theory, rather than a pure diffusion theory. An investigation of extending the numerical solution methodology of the standard diffusion theory to the solution of the generalized pinch-diffusion theory has been carried out. It is found that in the edge pedestal, where the inward pinch velocity is large in H-mode plasmas, a finer mesh spacing will be required than is necessary for similar accuracy farther inward, where the pinch velocity diminishes. An expression for the numerical error in various finite-differencing algorithms is presented.