Transient stability is an important measure in assessing a system's overall stability. It characterizes the ability of a power system to maintain stability following major disturbances.Modern power systems whose dynamics are increasingly complex and shaped by fast power electronic devices are testing the assumptions and limitations of existing transient stability simulation methods. This work presents a new method developed to improve transient stability simulation by extending its frequency bandwidth through dynamic phasors. This method constructs a continuous set of differential algebraic equations modeling a power system's dynamics using modified nodal analysis. These equations are numerically solved using a general purpose differential algebraic equations solver based on a variable step and variable order algorithm.This selection allows the method developed in this work to conduct accurate simulations while maintaining the advantages of demodulation in phasor-based analysis. Models are included for linear ac networks as well as two important components for power system simulation.