A New Shooting Method for Solving Boundary Layer Equations in Fluid Mechanics

In this paper, we propose a new method to tackle of two famous boundary layer equations in fluid mechanics, namely, the Falkner-Skan and the Blasius equations. We can employ this method to find unknown initial conditions. The pivotal point is based on the erection of a one-step Lie group element G(T) and the formation of a generalized mid-point Lie group element G(r). Then, by imposing G(T) = G(r) we can seek the missing initial conditions through a minimum discrepancy from the target in terms of a wight factor r is an element of (0. 1). Numerical examples are worked out to persuade that this novel approach has good efficiency and accuracy with a fast convergence speed by searching r with the minimum norm to fit two targets.