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Xu, Ding; Xu, Jinglei; Xie, Gongnan

Revisiting Blasius flow by fixed point method. (English) Zbl 1474.34082

Abstr. Appl. Anal. 2014, Article ID 953151, 9 p. (2014).
Summary: 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.

MSC:

34A45 Theoretical approximation of solutions to ordinary differential equations
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
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\textit{D. Xu} et al., Abstr. Appl. Anal. 2014, Article ID 953151, 9 p. (2014; Zbl 1474.34082)
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