To ensure a DC microgrid operates stably after a large disturbance, power converters should operate within acceptable voltage and current ranges during transient processes. However, it is challenging to develop a non-conservative stability analysis method that can consider power converter capacity. To address this problem, this paper presents a stability analysis procedure based on Lyapunov theory and numerical integration to evaluate large-signal stability and transient variations of physical variables such as duty cycle, voltage and current. Compared with some reported methods, the proposed method is less conservative and can describe the detailed dynamics of the system. The accuracy of the proposed method is verified by the case study of a single-bus DC microgrid.