Please use this identifier to cite or link to this item: https://ah.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:[應用數學系] 學位論文

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