Predicting the velocity, the temperature and the heat transfer rates within compressible boundary layers remains a challenging problem. Under compressibility and high Reynolds conditions, the density variations become very significant, resulting in high heat transfer rates. The net result is an altering of the dynamics within the boundary layer that is significantly different from its laminar counterpart. Physical properties, such as the specific heat capacities, the viscosity and the thermal conductivity, which are often considered constant, now vary with respect to temperature, creating a strong coupling between the velocity and the temperature fields. Despite the progress made in this field of research, a common issue frequently expressed in the literature is the difficulty in acquiring high quality time-resolved velocity and temperature data in compressible flows, especially near the wall. The major objective of this study is to demonstrate the capabilities of the Integral-Differential Scheme (IDS) by solving the flow field challenges within compressible boundary layers. It was demonstrated that IDS have the capability of accurately solving the full Navier-Stokes equations under realistic conditions. In the case of the compressible boundary layer, the IDS capture the flow field physics. However, it was demonstrated that the IDS is highly sensitive to grid resolution as well as the prescribed boundary conditions.