Solving a laminar boundary layer equation with the rational Gegenbauer functions

In this paper, a collocation method using a new weighted orthogonal system on the half-line, namely the rational Gegenbauer functions, is introduced to solve numerically the third-order nonlinear differential equation, af‴+ff″=0af‴+ff″=0, where a   is a constant parameter. This method solves the problems on semi-infinite domain without truncating it to a finite domain and transforming the domain of the problems to a finite domain. For a=2a=2, the equation is the well-known Blasius equation, which is a laminar viscous flow over a semi-infinite flat plate. We solve this equation by considering 1⩽a⩽21⩽a⩽2 and compare the new results with the established results to show the efficiency and accuracy of the new method.