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 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;Applicability Analysis of Homogeneous Balance Method in Solving Nonlinear Partial Differential Equations Authors: 呂東丞;Leu, Dong-Chen. Contributors: 物理學系 Keywords: 非線性系統;孤波;Nonlinear system;Soliton Date: 2018-08-22 Issue Date: 2018-08-31 13:57:59 (UTC+8) Publisher: 國立中央大學 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。;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. Appears in Collections: [物理研究所] 博碩士論文

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