Iterative Scheme for Solution to the Falkner-Skan Boundary Layer Wedge Flow Problem

We study Falkner-Skan boundary layer wedge flow problem of an incompressible viscous fluid and develop an iterative scheme, the generalized approximation method (GAM), to obtain a solution to the problem. By using similarity transformation, the nonlinear partial differential equation for the velocity field is transformed to a third order nonlinear ordinary differential equation. We provide estimates for the exact solution of the nonlinear problem. These estimates determine the region of existence of solution of the problem. Based on these estimates, we develop the generalized approximation method GAM for the solution of the problem. The GAM is a monotone iterative scheme which generates a bounded monotone sequence of solutions of linear problems. The sequence converges monotonically and rapidly to a solution of the original non- linear problem. We study the effect of the Falkner-Skan power-law parameter on the velocity field and the shear stress. For the numerical simulations, we use Mathematica.