基于不动点方法求解非线性Falkner-Skan流动方程  

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

作　　者：许丁[1] 谢公南[2] 

机构地区：[1]机械结构强度与振动国家重点实验室(西安交通大学),西安710049 [2]西北工业大学工程仿真与宇航计算实验室,西安710072

出　　处：《应用数学和力学》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~~

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.

关 键 词：Falkner-Skan流动 不动点方法 非线性微分方程 边值问题 

分 类 号：O351[理学—流体力学] TB126[理学—力学]