A numerical method for the solution of the Falkner-Skan equation
Applied Mathematics and Computation
A finite-difference method for the Falkner-Skan equation
Applied Mathematics and Computation
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The Blasius and Falkner-Skan equations arise in the study of laminar boundary layers exhibiting similarity. In this paper, the mathematical models for steady boundary layer flow past a horizontal flat plate and a semi-infinite wedge are considered. The nonlinear partial differential equations consisting of two independent variables are solved in the power series form. The radii of convergence of the solutions of the Blasius and Falkner-Skan equations are presented using the Domb-Sykes plot. The solution of the Falkner-Skan equation is based on the improvement of the perturbation series, which diverges beyond a certain radius, by means of the iterated Shanks transformation. The effectiveness of the method is illustrated by applying it successfully to various instances of the Falkner-Skan equation.