Solving a laminar boundary layer equation with the rational Gegenbauer functions

摘要

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" = 0, where a is a constant parameter. Thjs 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 = 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 ≤ 2 and compare the new results with the established results to show the efficiency and accuracy of the new method.