Growing In Falkner-skan Equation Numerical Solution

Falkner-Skan equation is a typical equation in the boundary layer flow prob-lems, which is a nonlinear ordinary differential equation defined on a semi-infinite interval. In this paper, some research is done and a new algorithm is proposed to solve it numerically. First of all, a freely moved boundary parameterη∞is introduced to truncate the original semi-infinite interval[0,∞] into a finite interval[0,η∞]. Based on which, the shooting method can be used. However, we do not apply the shooting method on the equation directly. In contrast, in order to better use the shooting method, we make the following preparation:we split the modified equation which still remains nonlinear into two linear equations with lower order, first-order and second-order. As for the first-order equation, we treat it analytically, while we use truncated Taylor expansion to approximate the second-order one. At last, we adopt nested secant iteration to update the 'shooting angle', namely a:f＂(0). In the last section, we provide the numerical results as well as the comparison between our results and the data reported by the literature. From which, we can see the method is effective and efficient.