This research is concerned with developing computationally very efficient methods for solving inverse problems for elliptic and mixed type differential equations, in particular the equations of compressible fluid flow around an unknown body. The unknown body is to be recovered from specific pressure distribution along the unknown body. An appropriate formulation of the problem reduces it to solving a single nonlinear boundary value problem. For generating supercritical airfoils the scheme uses an iterative method based on the solution of the elliptic and the hyperbolic problems in their respective domains.
