研究生: |
王文光 Wang Wen-Kuang |
---|---|
論文名稱: |
一些三階非線性微分方程之解法 Methods for solving some third-order nonlinear differential equations |
指導教授: |
郭忠勝
Guo, Jong-Shenq |
學位類別: |
博士 Doctor |
系所名稱: |
數學系 Department of Mathematics |
論文出版年: | 2002 |
畢業學年度: | 90 |
語文別: | 英文 |
論文頁數: | 18 |
中文關鍵詞: | 非線性微分方程 、三階 |
英文關鍵詞: | nonlinear differential equations, third-order |
論文種類: | 學術論文 |
相關次數: | 點閱:96 下載:6 |
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我們提供兩種方法解決三階非線性微分方程。第一、利用 shooting 的方法來解決。第二、使用二維的 shooting 方法及一個由 McLeod 和 Serrn 所做的拓樸結果解決第二個問題。
We survey two methods for solving some third-order differential
equations. First, using the shooting method to study the
problem. Second, using two-dimensional shooting method and a topological result of McLeod and Serrn to study the second problem.
[1]{BP} F. Bernis and L.A. Peletier, Two problems from draining flows involving third-order ordinary differential equations. Siam. J. Math. Anal. 27 (1996) 515-527.
[2]{T} W.C. Troy, Solutions of third-order differential equations relevant to draining and coating flows, Siam J. Math. Anal. 24 (1993), 155-171.
[3]{BPW} F. Bernis and L.A. Peletier and S.M. Williams, Source type solutions of a fourth order nonlinear degenerate parabolic eqnation. Nonlinear Anal. 18 (1992) 217-234.
[4]{MS} J.B. McLeod and J. Serrin, The existence of similar solutions for some laminar boundary layer equations, Arch. Rational Mech. Anal. 31(1968), 288-303.