An iterative method for solving the Falkner–Skan equation

We propose a new iterative method to solve the boundary value problems (BVPs) of the Falkner–Skan equation over a semi-infinite interval. In our approach, we use the free boundary formulation to truncate the semi-infinite interval into a finite one. Then we use the shooting method to transform the BVP into initial value problems (IVPs). In order to find the “shooting angle” and the unknown free boundary, a modification of the classical Newton’s method is used where the Jacobian matrix can be accurately obtained by solving another two IVPs. To illustrate the effectiveness of our method, we compare our numerical results with those obtained by previous methods under various instances of the Falkner–Skan equation.