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We present a method to model organic light-emitting devices driven by a current source in the context of drift-diffusion models. The method is extended to the case of voltage excitation, and calculations with current and voltage excitation are compared. An advantage over the application of Poisson's equation is that standard numerical solvers can be used for the ordinary differential equations that result from the spatial discretization of the model equations. We employ the model to calculate I- V characteristics and to examine the transient response of an organic light-emitting diode under pulsed current operation. The approach is generalized to the case of an arbitrary number of layers.