博碩士論文 953202006 詳細資訊




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姓名 莊凱迪(Kai-Ti Chuang)  查詢紙本館藏   畢業系所 土木工程學系
論文名稱 Blatz-Ko圓對稱波方程差分式的群分析
(Group analysis of the finite difference schemes for the Blatz-Ko spherical wave equation)
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摘要(中) 本論文主要研究Blatz-Ko材料圓形對稱動態波方程式,將非線性偏微分方程轉換至非線性常微分方程,使得求解過程簡化,再經由李群理論推導波方程各種的等值表示式與差分式,並利用Euler方法,Lax方法,Lax-Wendroff方法推導波方程各個差分式組合,各個差分式組合給予邊界條件,來觀察與分析最大誤差值,穩定特性,一致特性,準確特性。
摘要(英) This thesis investigates the symmetry properties of the finite difference schemes for the spherical wave equation for Blatz-Ko materials. We use the Euler method, Lax method and Lax-Wendroff method to derive difference schemes and investigate their group properties. The maximum error, stability, consistency and precision of these schemes are analyzed.
關鍵字(中) ★ Blatz-Ko材料
★ 圓對稱差分式
★ 波方程
★ 群的分析
關鍵字(英) ★ the finite difference schemes
★ Group analysis
★ Blatz-Ko spherical wave equation
論文目次 摘要 Ⅰ
英文摘要 II
誌謝 Ⅲ
目錄 Ⅳ
表目錄 Ⅵ
圖目錄 Ⅶ
第一章緒論 1
第二章 Blatz-Ko圓形波方程及其李群 3
第三章 Blatz-Ko圓形波方程等值表示式的李群 7
第四章 Blatz-Ko圓形波方程差分式的李群 10
4-1 Euler顯式差分式 11
4-2 Lax差分式 13
4-3 Lax-Wendroff差分式 14
第五章 Blatz-Ko圓形波方程差分式之數值分析 16
5-1 前言 16
5-2 Euler scheme 分析 18
5-2-1 Euler scheme (4.4)式之數值計算 18
5-2-2 Euler scheme (4.5)式之數值計算 21
5-3 Lax scheme 分析 24
5-3-1 Lax scheme (4.7)式之數值計算 24
5-3-2 Lax scheme (4.8)式之數值計算 27
5-4 Lax-Wendroff 分析 31
5-4-1 Lax-Wendroff (4.9)式之數值計算 31
5-4-2 Lax-Wendroff(4.11)式之數值計算 32
第六章結論 107
結論 109
參考文獻 108
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指導教授 李顯智(Hsien-Chih Lei) 審核日期 2008-7-22
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