博碩士論文 103222039 完整後設資料紀錄

DC 欄位	值	語言
DC.contributor	物理學系	zh_TW
DC.creator	呂東丞	zh_TW
DC.creator	Dong-Chen. Leu	en_US
dc.date.accessioned	2018-8-22T07:39:07Z
dc.date.available	2018-8-22T07:39:07Z
dc.date.issued	2018
dc.identifier.uri	http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=103222039
dc.contributor.department	物理學系	zh_TW
DC.description	國立中央大學	zh_TW
DC.description	National Central University	en_US
dc.description.abstract	在近代科學研究中，非線性效應的影響越來越不可忽略，非線性偏微分方程式的重要性也隨之提高。但大多非線性系統不是絕對可解模型，因此研究學者發展了不少數學方法來解析非線性偏微分方程式。 在本文中我們主要使用齊次平衡解析法（Homogeneous Balance Method），希望找出除了數值模擬以外的方法求解非線性方程式。在此研究中我們利用解析解與數值模擬做比對，並以一常見的絕對可解模型－KdV方程式作為基準。 研究中發現，不同的初始條件會造成不同的精準度。而齊次平衡方法在除了孤波之外的計算並無法表現色散現象以及非線性現象的特徵。希望由此研究結果確認此方法的可信度或可使用的範圍，以加速往後對非線性系統的運算。	zh_TW
dc.description.abstract	In nowadays scientific researches, the nonlinear effects become non ignorable. Therefore, the technique for solving nonlinear partial differential equations is indispensable. Most nonlinear partial differential equations are not exact solvable, therefore, many researchers are trying to develop different other methods for solving these problems. In this study, the applicability of the homogeneous balance method in solving partial differential equations was examined by comparing the analytical results with the numerical simulation which based on finite - difference time - domain method. This work can provide a guideline for the application of the homogeneous balance method in solving partial differential equations with various parameter space and initial conditions.	en_US
DC.subject	非線性系統	zh_TW
DC.subject	孤波	zh_TW
DC.subject	Nonlinear system	en_US
DC.subject	Soliton	en_US
DC.title	齊次平衡解析方法在求解非線性偏微分方程式的適用性分析	zh_TW
dc.language.iso	zh-TW	zh-TW
DC.title	Applicability Analysis of Homogeneous Balance Method in Solving Nonlinear Partial Differential Equations	en_US
DC.type	博碩士論文	zh_TW
DC.type	thesis	en_US
DC.publisher	National Central University	en_US