Author(s): XU Ding, XIE Gong-nan, State Key Laboratory for Strength and Vibration of Mechanical Structures, Engineering Simulation and Aerospace Computing, Northwestern Polytechnical University
Pages: 78-86
Year: 2015 Issue:  1
Journal: Applied Mathematics and Mechanics
Keyword:  Falkner-Skan flow; fixed point method; nonlinear differential equation; boundary value problem;
Abstract: The Falkner-Skan flowequation is a strongly nonlinear differential equation,which describes the flowaround a wedge. In order to overcome the difficulties originated from the semi-infinite interval and asymptotic boundary condition in this flowproblem,transformations were simultaneously conducted for both the independent variable and the correponding function to convert the problem to a 2-point boundary value one within a finite interval. The deduced new-form nonlinear differential equation was subsequently solved with the fixed point method( FPM). The present analytical results obtained with the FPM agree well with the previous referential numerical ones. The accuracy of the present solution is conveniently improved through iteration under the FPM framework,which shows that the FPM makes a promising tool for nonlinear differential equations.