On A Numerical Treatment of The Falkner–Skan Equation

Arwa Hajjari

Cairo University, Cairo, Egypt

Abstract

This paper presents an iterative method based on spline function approximations for the numerical solution of the Falkner–Skan equation (FSE) over a semi-infinite interval. This technique will transform the FSE into two initial value problems, so the solution of FSE will be reduced from the interval [0,¥[ into [0,1]. Spline approximations are applied directly to the FSE without its reducing into a system of first-order differential equations, thus, the algorithm of spline method has a computational cost that is cost-effective. The spline solution of the FSE is existent and unique, and the convergence analysis for the spline method applied to the FSE is discussed. Numerical results are compared with those obtained by previous methods under various instances of the FSE. The comparisons show the accuracy and efficiency of the presented methodology.

Keywords: Numerical approximation; differential equation; Falkner-Skan equation