Solution of Falkner-Skan equation with heat transfer using a Legendre collocation method

In this paper, we introduce a new spectral collocation method for solving the Falkner-Skan equation with heat transfer. The Falkner-Skan equation is a nonlinear third-order boundary value problem on semi-infinite domain. The properties of the Legendre polynomials are used to approximate an unknown function and its integrals. Then the shifted Legendre-Gauss points are utilized as the collocation points to reduce the problem to the solution of an algebraic system. The results show that the proposed method delivers a solution with high accuracy and very rapid convergence. Comparisons with other methods in the literature demonstrate the applicability and accuracy of the proposed method.

Falkner-Skan equation, collocation method, shifted Legendre-Gauss points, semi-infinite domain