4. METHOD OF SOLUTION
The design program results from the ability to solve the partial differential equations of two-dimensional inviscid gas dynamics and analytic continuation into the domain of two independent complex characteristic coordinates. The domain of integration is mapped conformally onto the unit circle in the plane of one of these coordinates. On the circle it is possible to formulate a boundary value problem for the stream function that is well-posed even in the case of transonic flow. Two boundary value problems are solved by means of the fast Fourier Transform and complex extension. Thus, a procedure is developed for the calculation of an airfoil on which the speed q is prescribed as a function of arc length s. For subsonic flow an exact solution of this non-linear problem is obtained. For the transonic case a shockless flow results which assumes the assigned subsonic values of the speed q exactly but the resulting supersonic values of speed are near the given values.