An inverse method to solve the compressible turbulent boundary layer with separation using the boundary layer equations is presented. The results indicate that a reasonable solution can be obtained at far less computation time than solving the Navier-Stokes equation within comparable accuracy. Prandtl's mixing length model for turbulence is introduced and numerical instabilities in reverse flow region are removed by using the Reyhner-Fl$\ddot{u}$gge-Lotz approximation. Keller box scheme is introduced to discretize and solve the boundary layer equations.
To demonstrate the applicability of the present approach, the results are compared with experimental or another numerical ones.
