An accurate and efficient method for the numerical computation of boundary layer flows is developed. The finite-difference approximation of the differential equation uses the grid point values of the function and of the first derivative. In order to obtain the finite-difference schemes of higher order the collocation method of Falk is applied with Hermitian interpolating polynomials. This results in a system of finite-difference equations for the unknown function and first derivative. The equations are solved by means of a Gaussian elimination procedure. In order to verify the accuracy and efficiency of this finite-difference method of Hermitian type an ordinary differential equation of second order is solved as a test example. Then this technique is applied to equations of boundary layer flows, in particular to the Falkner-Skan equation and to Howarth's retarded flow. Numerical results are presented for each test example. Comparisons with results of other authors indicate a gain in accuracy for the finite-difference method of Hermitian type.
