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The equations that govern the behavior of steel under-going reduction are complex differential equations. A method of solving these equations using a hybrid computer is described, and the peculiar problems associated with such a solution are discussed. In the hybrid implementation, differential equations can be solved very fast, and the speed of solution is governed by the number of samples one requires of the trajectory from the analog computer for useful computation in the digital computer. Thus, methods are described whereby the number of samples taken can be reduced and the accuracy of the manipulations performed by the digital computer can still be maintained. The results obtained are both accurate and rapid, and the system has the normal engineering appeal of a purely analog solution.