Derivation of discretely coincident forms of continuous linear time-invariant models using the transfer function approach

Three discrete forms of the continuous models are discussed, namely, finite-difference approximations, discretely coincident forms and discrete analogies. The transfer function approach to the derivation of discretely coincident forms of continuous models is developed. The Muskingum flood-routing model, the cascade of equal linear reservoirs and simple cascades of unequal direct and inverse elements are used as examples to demonstrate the method. The significance of the discretely coincident forms of continuous models in the interpretation of the discrete stochastic models of time series analysis is also examined.