The stability of stagnation point flow has long been recognized as an important problem in aerodynamic analysis. Boundary layer disturbances located near the stagnation line can have a significant effect on the overall properties of an airfoil. One example of current interest is the analysis of unsteady multi-phase stagnation flows for application to problems involving aircraft icing. In this study, numerical methods which can be used to address the stability and non-parallel unsteady development of such stagnation point problems are investigated for linearized single phase aerodynamic flows using both two-dimensional and three-dimensional methods. A streamfunction-vorticity formulation is evaluated for two-dimensional linearized stagnation flows. In addition, a primitive variable formulation is developed for three-dimensional linearized stagnation flows. The two methods are tested for grid refinement, and results obtained using the three-dimensional method are compared with those from the two-dimensional method. As expected, it is found that three-dimensional disturbances decay at a faster rate than two-dimensional ones.