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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/80284


    Title: 二階非線性微分方程與應用
    Nonlinear differential equation of second order and its applications
    Authors: 陳仁發
    Chen, Ren Fa
    Contributors: 李明融
    Li, Meng Rong
    陳仁發
    Chen, Ren Fa
    Keywords: Nonlinear 2nd Order Differential Equation
    Mathematical Model
    二階非線性微分方程
    數學模型
    Date: 2015
    Issue Date: 2016-01-04 16:52:14 (UTC+8)
    Abstract: 在這篇論文當中，我們引用"海岸綠堤--水筆仔`網站上的研究資料並且藉由Matlab程式軟體的幫助建構數學模型，我們討論以下的二階非線性微分方程
    (i) u``(t)=f(u(t)), u(t_0)=u_0, u`(t_0)=u_1.
    (ii) u``(t)=f(u`(t)), u(t_0)=u_0, u`(t_0)=u_1.
    我們比較拋物線函數，立方函數，傅立葉和函數，正弦和函數並且從這些函數中選出最好的一個當作我們的模型，我們得到一些主要的結果。
    In this paper, we use the real data from website of "Seacoast Green Bank--Kandelia` and construct mathematical models with the help of Matlab, we discuss the following nonlinear 2nd order differential equation
    (i) u``(t)=f(u(t)), u(t_0)=u_0, u`(t_0)=u_1.
    (ii) u``(t)=f(u`(t)), u(t_0)=u_0, u`(t_0)=u_1.
    We compared with the functions of parabolic, cubic, Fourier summation, sum of sine and choose the best one from them as our model, we have obtained main results.
    謝辭 i
    中文摘要 ii
    Abstract iv
    Contents vi
    List of Figures viii
    List of Tables ix
    1 Introduction 1

    2 Model Construction From Real Data 2
    2.1 Sourse . . . . . . . . . . . . . . . . . . . . . 2
    2.2 Time and Height . . . . . . . . . . . . . . . . . 5

    3 Mathematical Models 7
    3.1 Some methods . . . . . . . . . . . . . . . . . . 7
    3.2 Model 1 . . . . . . . . . . . . . . . . . . . . . 7
    3.3 Model 2 . . . . . . . . . . . . . . . . . . . . 10
    3.4 Model 3 . . . . . . . . . . . . . . . . . . . . 11

    4 Some Fundamental Theorem 14
    4.1 Conservation law of Model 1 . . . . . . . . . . 14
    4.2 Estimate for u(t) . . . . . . . . . . . . . . . 18

    5 Conclusion 22

    A 24
    A.1 PART 1 . . . . . . . . . . . . . . . . . . . . . 24
    A.2 PART 2 . . . . . . . . . . . . . . . . . . . . . 29

    Bibliography 34
    Reference: [1] J.D. Murray. Mathematical biology. I. An introduction Springer-Verlag New York, 2002.

    [2] R. P. Agarwal and D. O’Regan. An Introduction to Ordinary Differential Equations. Springer, New York, 2008.

    [3] Ferdinand Verhulst. Nonlinear Differential Equations and Dynamical Systems. Springer-Verlag Berlin Heidelberg, 1990.

    [4] 徐詩芸(2013), 互花米草在關渡自然保留區的擴散評估與模擬, 國立臺灣大學地理環境資源學研究所碩士論文.

    [5] 海岸綠堤–水筆仔. http://163.20.52.80/stu635/cwpspage/mang/study/index.htm.

    [6] 洪維恩. Matlab 程式設計-第二版. 旗標出版股份有限公司, 西元2013 年8 月出版.
    Description: 碩士
    國立政治大學
    應用數學系
    101751005
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G1017510051
    Data Type: thesis
    Appears in Collections:[Department of Mathematical Sciences] Theses

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