A study of numerical solutions to the linear wave equation and the parabolic wave equation is presented. Finite-difference, time-domain methods are used to calculate the acoustic field emitted from a phased diagnostic ultrasound transducer in a non-attenuating medium. Results are compared to Field II, a simulation package that has been used extensively to linearly model transducers in ultrasound. The simulation of the parabolic equation can accurately predict the lateral beamplot for large f/#s, but, it exhibits 2-3 dB errors for small f/#s. It also overestimates the depth at which the focus occurs. For the considered array, it is shown that the finite-difference solution of the wave equation is accurate for a small and large f/#. The lateral beamplots and axial intensities are in excellent agreement with the Field II simulations.