We propose a method to simulate the transition process of endogenous growth models. Different to existing procedures, this method requires the original, unscaled system of differential equations as the only input. It merely has to fulfill sufficient conditions which are satisfied by every existing model of economic growth. Therefore, this algorithm can simulate growth models, for which the analytical calculation of the balanced growth rate is too complicated or even impossible. Internally the algorithm conducts the scaling of the Lucas (1988) model in a general way. By computing the balanced growth rates numerically, the analytical connection to the underlying parameters can be unspecified. In addition, theoretical properties of scale-adjustment are investigated in detail.