Application of the Fixed Point Method to Solve the Nonlinear Falkner-Skan Flow Equation

XU Ding; XIE Gong-nan

doi:10.3879/j.issn.1000-0887.2015.01.007

Volume 36 Issue 1

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XU Ding, XIE Gong-nan. Application of the Fixed Point Method to Solve the Nonlinear Falkner-Skan Flow Equation[J]. Applied Mathematics and Mechanics, 2015, 36(1): 78-86. doi: 10.3879/j.issn.1000-0887.2015.01.007

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Application of the Fixed Point Method to Solve the Nonlinear Falkner-Skan Flow Equation

doi: 10.3879/j.issn.1000-0887.2015.01.007

XU Ding¹,
XIE Gong-nan²

¹State Key Laboratory for Strength and Vibration of Mechanical Structures(Xi’an Jiaotong University), Xi’an 710049, P.R.China;²Engineering Simulation and Aerospace Computing (ESAC),Northwestern Polytechnical University, Xi’an 710072, P.R.China

Funds: The National Natural Science Foundation of China(11102150)

Received Date: 2014-07-16
Publish Date: 2015-01-15

Abstract

Abstract

The Falkner-Skan flow equation is a strongly nonlinear differential equation, which describes the flow around a wedge. In order to overcome the difficulties originated from the semi-infinite interval and asymptotic boundary condition in this flow problem, 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.
- Falkner-Skan flow,
- fixed point method,
- nonlinear differential equation,
- boundary value problem

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References(23)

References

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