Powerful propagation-prediction tools, based on the split-step Fourier-transform and the Finite-Element-Method (FEM) solutions of the parabolic equation (PE) are discussed. The parabolic equation represents one-way propagation, and is widely used in two-dimensional (2D) groundwave propagation modeling. It takes the Earth's curvature, the atmospheric refractivity variations, non-flat terrain scattering, and the boundary losses into account. MATLAB-based numerical split-step parabolic-equation and Finite-Element-Method parabolic-equation routines were developed. These were used in canonical tests and comparisons to illustrate that the parabolic equation accounts for all of these effects. Both tools were calibrated against an analytical exact solution.