Abstract
The main feature of the boundary layer flow problems, such as Blasius and Falkner-Skan problems, is the inclusion of the boundary conditions at infinity. As a well known fact, such boundary conditions cause difficulties for any of the series methods. This is because the boundary conditions at infinity can not be imposed directly into the series solution, where Pade approximant should be first constructed before applying such conditions. To overcome this difficulty, an approach has been suggested recently by Ebaid and Al-Armani [Abstr. Appl. Anal., 753049 (2013)], which is based on changing the boundary conditions at infinity to classical ones by using a proper transformation. This approach is applied in the present paper to solve a class of Falkner-Skan equation analytically and numerically. Moreover, an exact solution is deduced at a certain value of the velocity ratio parameter. In addition, the current numerical results are compared with the other existing solutions, and good agreement has been achieved. Indeed, the main advantage of the present approach is the complete avoidance of Pade approximant to deal with the boundary condition at infinity.