摘要
Falkner-Skan流动方程描述绕楔面的流动,该方程具有很强的非线性.首先通过引入变换式,将原半无限大区域上的流动问题转化为有限区间上的两点边值问题.接着基于泛函分析中的不动点理论,采用不动点方法求解两点边值问题从而得到Falkner-Skan流动方程的解.最后将不动点方法给出的结果和文献中的数值结果相比较,发现不动点方法得到的结果具有很高的精度,并且解的精度很容易通过迭代而不断得到提高.表明不动点方法是一种求解非线性微分方程行之有效的方法.
The Falkner-Skan flow equation is describes the flow around a wedge. In order a strongly nonlinear differential equation, which 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 refer- ential numerical ones. The accuracy of the present solution is conveniently improved through it- eration under the FPM framework, which shows that the FPM makes a promising tool for nonlinear differential equations.
出处
《应用数学和力学》
CSCD
北大核心
2015年第1期78-86,共9页
Applied Mathematics and Mechanics
基金
国家自然科学基金(11102150)
中央高校基本科研业务费专项资金~~
作者简介
许丁（1980-），男，西安人，讲师，博士（通讯作者．E-mail：dingxu@mail．xjt．edu．cn）．
