二階非線性微分方程與應用

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 \r\n(i) u``(t)=f(u(t)), u(t_0)=u_0, u`(t_0)=u_1.\r\n(ii) u``(t)=f(u`(t)), u(t_0)=u_0, u`(t_0)=u_1.\r\n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\r\n(i) u``(t)=f(u(t)), u(t_0)=u_0, u`(t_0)=u_1.\r\n(ii) u``(t)=f(u`(t)), u(t_0)=u_0, u`(t_0)=u_1.\r\nWe 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\r\n中文摘要 ii\r\nAbstract iv\r\nContents vi\r\nList of Figures viii\r\nList of Tables ix\r\n1 Introduction 1\r\n\r\n2 Model Construction From Real Data 2\r\n2.1 Sourse . . . . . . . . . . . . . . . . . . . . . 2 \r\n2.2 Time and Height . . . . . . . . . . . . . . . . . 5\r\n\r\n3 Mathematical Models 7\r\n3.1 Some methods . . . . . . . . . . . . . . . . . . 7\r\n3.2 Model 1 . . . . . . . . . . . . . . . . . . . . . 7 \r\n3.3 Model 2 . . . . . . . . . . . . . . . . . . . . 10\r\n3.4 Model 3 . . . . . . . . . . . . . . . . . . . . 11\r\n\r\n4 Some Fundamental Theorem 14 \r\n4.1 Conservation law of Model 1 . . . . . . . . . . 14\r\n4.2 Estimate for u(t) . . . . . . . . . . . . . . . 18\r\n\r\n5 Conclusion 22\r\n\r\nA 24\r\nA.1 PART 1 . . . . . . . . . . . . . . . . . . . . . 24\r\nA.2 PART 2 . . . . . . . . . . . . . . . . . . . . . 29\r\n\r\nBibliography 34