### 博碩士論文 100221027 完整後設資料紀錄

 DC 欄位 值 語言 DC.contributor 數學系 zh_TW DC.creator 吳峙霆 zh_TW DC.creator Chih-Ting Wu en_US dc.date.accessioned 2013-7-29T07:39:07Z dc.date.available 2013-7-29T07:39:07Z dc.date.issued 2013 dc.identifier.uri http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=100221027 dc.contributor.department 數學系 zh_TW DC.description 國立中央大學 zh_TW DC.description National Central University en_US dc.description.abstract 在本文中，我們將考察具柯氏力項的二維非線性淺水波方程有限差分數值解。利用二階Runge-Kutta法與算子拆解法對時間變數進行離散化，我們推導出兩種Lax-Wendroff類型的有限差分數值解法，這兩種方法在時間與空間變數的離散上均能維持二階的精確度。我們將選取反射型的邊界條件及數種不同的初始條件進行一系列的數值模擬實驗。經過大量的數值模擬後，我們發現以Runge-Kutta法為基礎的Lax-Wendroff有限差分數值解似乎具較高的穩定性。 zh_TW dc.description.abstract In this thesis, we will investigate the finite difference schemes for solving the 2-D nonlinear shallow water equations with the Coriolis effect. Based on the second-order Runge-Kutta method and the operator-splitting method for time discretization, we derive two Lax-Wendroff-type finite difference schemes. Both proposed finite difference schemes possess the second-order accuracy in temporal and spatial variables. We will apply the reflective boundary condition with various initial conditions to perform a series of numerical simulations. From the numerical results, we find that the proposed scheme based on the Runge-Kutta method seems having a better stability. en_US DC.subject 淺水波方程 zh_TW DC.subject 柯氏力 zh_TW DC.subject Lax-Wendroff差分法 zh_TW DC.subject Runge-Kutta法 zh_TW DC.subject 算子拆解法 zh_TW DC.subject shallow water equations en_US DC.subject Coriolis effect en_US DC.subject Lax-Wendroff scheme en_US DC.subject Runge-Kutta method en_US DC.subject operator-splitting method en_US DC.title 二維非線性淺水波方程的Lax-Wendroff差分數值解 zh_TW dc.language.iso zh-TW zh-TW DC.title Lax-Wendroff Difference Solutions of the 2-D Nonlinear Shallow Water equations en_US DC.type 博碩士論文 zh_TW DC.type thesis en_US DC.publisher National Central University en_US