馮.卡門旋轉(zhuǎn)流方程及馬丟方程的同倫分析

1、上海交通大學(xué)碩士學(xué)位論文馮.卡門旋轉(zhuǎn)流方程及馬丟方程的同倫分析姓名：楊承申請學(xué)位級別：碩士專業(yè)：船舶與海洋結(jié)構(gòu)物設(shè)計(jì)制造指導(dǎo)教師：廖世俊20031201ABSTRACTIn this thesis, two kinds of differential equations are analysed by the Homotopy Anal- ysis Method(HAM), which is a kind of analytic met

2、hod proposed to give analytic solutions for nonlinear problems.Firstly, Von K´ arm´ an swirling viscous flow , one of the classic problems in fluid mechanics is solved by the HAM. Von K´ arm´ an swirl

3、ing viscous flow is a set of coupled ordinary differential equations with strong nonlinearity, the analytic solutions given by HAM in this thesis, which is the first purely analytic solution for this classic problem, con

4、verge well and agree well with numerical solutions.Secondly, Mathieu Equation, a linear ordinary differential equations with varia- tional coefficient, is solved by HAM. It is also very difficult for other methods to giv

5、e analytic solutions of this linear equation. In this thesis, the analytic expression of the Eigenvalue and Eigenfunction of Mathieu Equation is given by HAM which agree well with numerical results and the linear problem

6、 homotopy-Pad´ e technique is employed to enhance the convergence.So the efficiency of HAM is proved by the successful analysis of these two different equations and the its application field is broadened.Key Words V