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 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 EquationMathematical 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: [應用數學系] 學位論文

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