Solving a laminar boundary layer equation with the rational Gegenbauer functions

Abstract 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. 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 = 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.

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