Modeling in terms of cell dynamical systems (CDS) is advocated as an efficient tool to sort out correct guesses about the mathematical essence of macroscopic nonlinear phenomena with space-time patterns. CDS is a map from a discrete pattern at time t to the one at t+1. With the aid of segregation processes, the CDS modeling is illustrated. Numerical schemes are introduced which are often stable for fairly large increments to bridge conventional partial differential equation (PDE) models and CDS models. Although these schemes with large increments usually do not give correct solutions to the original PDE, they could still give quantitatively accurate results for macroscopic observables. Thus it is meaningful to discuss qualitatively accurate schemes.