Numerical Solution of the Falkner-Skan Equation Arising in Boundary Layer Theory Using the Sinc-Collocation Method

Abstract

We consider the numerical solution of the well known Falkner-Skan problem, which is third order nonlinear boundary value problem. The approach we are going to follow is to first transform the third order boundary value problem on the semi-finite domain into a second order nonlinear boundary value problem on a finite domain through introducing a special transformation. The resulting two-point boundary value problem is then treated numerically using the sinc-collocation method which is known to converge exponentially. Numerical results will be presented for various values of the parameters representing various types of flows. Comparison with the work of others will also be done to show the accuracy of the Sinc method.