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
Citation: 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

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

doi: 10.3879/j.issn.1000-0887.2015.01.007
Funds:  The National Natural Science Foundation of China(11102150)
  • Received Date: 2014-07-16
  • Publish Date: 2015-01-15
  • 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.
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