We introduce a new numerical approach to step flow growth, making use of its analogies to dendritic growth. Concentrating on the situation close to the instability threshold of step growth, nonlinear evolutionary equations for the steps on a vicinal surface can be derived in a multiple-scale analysis. This approach retains the relevant nonlinearities sufficiently close to the threshold. Our simulations recover and visualize these findings. However, on the basis of our simulations we further report results on the behaviour far from the threshold. Step propagation is treated as a moving-boundary problem based on the Burton-Cabrera-Frank (Burton W K, Cabrera N and Frank F C 1951 Phil. Trans. R. Soc. A 243 299) model. Our method handles the problem in a fully dynamical manner without any quasistatic approximations. Furthermore, it allows for overhangs.