AbstractThe applicability of a finite element‐differential method to the computation of steady two‐dimensional low‐speed, transonic and supersonic turbulent boundary‐layer flows is investigated. The turbulence model chosen for the Reynolds shear stress and turbulent heat flux is theK‐ϵ two‐equation model. Calculations are extended up to the wall and the exact values of the dependent variables at the wall are used as boundary conditions. A number of transformations are carried out and the assumed solutions at a longitudinal station are represented by complete cubic spline functions. In essence, the method converts the governing partial differential equations into a system of ordinary differential equations by a weighted residuals method and invokes an ordinary differential equation solver for the numerical integration of the reduced initial‐value problem. The results of the computations reveal that the method is highly accurate and efficient. Furthermore, the accuracy and applicability of thek‐ϵ turbulence model are examined by comparing results of the computations with experimental data. The agree