Mathematical model of the flow around airfoil with energy high-lift devices

In this work we give a system of integro-differential equations of a mathematical model of the airfoil with exhaust of an external flow at the upper surface of the airfoil and with a jet blow from the rear edge in its nonlinear nonstationary formulation. We show that for a singular integral equation which is present in this system we must seek a solution in the class of functions which are singular at the exhaust point of an external flow. We give the method of solving numerically this system, which is a development of the method of discrete vortices, as applied to the particular problem. We give examples of calculations.