An efficient numerical solution algorithm is presented for solving the interacting supersonic laminar boundarylayer problem. The method employs a time dependent approach with the alternating direction implicit (ADI) scheme and directly accounts for the necessary downstream boundary condition. Solutions are presented for MOO = 3 cold wall boundary-layer flow over a family of compression ramps with regions of reverse flow. Good comparison is given with experimental data and Navier-Stokes solutions for M^ =4 and 6, adiabatic wall, separated flow up a 10° compression ramp.