| 基于不动点方法求解非线性Falkner-Skan流动方程 |
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| 引用本文： | 许丁,谢公南. 基于不动点方法求解非线性Falkner-Skan流动方程[J]. 应用数学和力学, 2015, 36(1): 78-86. DOI: 10.3879/j.issn.1000-0887.2015.01.007 |
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| 作者姓名： | 许丁 谢公南 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金(11102150)；中央高校基本科研业务费专项资金 |
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| 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.
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| 关 键 词： | Falkner-Skan流动 不动点方法 非线性微分方程 边值问题 |
| 收稿时间： | 2014-07-16 |
Application of the Fixed Point Method to Solve the Nonlinear Falkner-Skan Flow Equation |
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| Affiliation: | 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 |
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| 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. |
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