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Abstract and Applied Analysis
Volume 2014, Article ID 953151, 9 pages
Research Article

Revisiting Blasius Flow by Fixed Point Method

1State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, No. 28, Xianning West Road, Xi'an 710049, China
2School of Jet Propulsion, Beijing University of Aeronautics and Astronautics, Xueyuan Road, No. 37, Beijing 100191, China
3School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China

Received 28 October 2013; Revised 7 December 2013; Accepted 7 December 2013; Published 12 January 2014

Academic Editor: Mohamed Fathy El-Amin

Copyright © 2014 Ding Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The well-known Blasius flow is governed by a third-order nonlinear ordinary differential equation with two-point boundary value. Specially, one of the boundary conditions is asymptotically assigned on the first derivative at infinity, which is the main challenge on handling this problem. Through introducing two transformations not only for independent variable bur also for function, the difficulty originated from the semi-infinite interval and asymptotic boundary condition is overcome. The deduced nonlinear differential equation is subsequently investigated with the fixed point method, so the original complex nonlinear equation is replaced by a series of integrable linear equations. Meanwhile, in order to improve the convergence and stability of iteration procedure, a sequence of relaxation factors is introduced in the framework of fixed point method and determined by the steepest descent seeking algorithm in a convenient manner.