1. National Taiwan Ocean University MSVLAB Department of Harbor and River Engineering 1 一端固定一端自由之 有限域繩波 Jia-Nan Ke ( 柯佳男 ) Reporter: Jia-Nan Ke ( 柯佳男 ) Jeng-Tzong Chen Advisor: Jeng-Tzong Chen ( 陳正宗 終身特聘教授 ) ( 陳正宗 終身特聘教授 ) 2007 創意教學 ─ 偏微分方程之波動動畫 2007.05.29

2. MSVLAB National Taiwan Ocean University Department of Harbor and River Engineering 2 Formulation of the problem x f(x) 13 6 Governing equation: free fixed Boundary condition: Initial condition:

3. MSVLAB National Taiwan Ocean University Department of Harbor and River Engineering 3 Method 1: Fourier Method 由 B. C. 利用時空分離的觀念，將波動方程的解假設為：

4. MSVLAB National Taiwan Ocean University Department of Harbor and River Engineering 4 Method 2: Image Method Original Image x f(x) 1 3 6 free fixed -3 911 -9 -11 15 13 -6

5. MSVLAB National Taiwan Ocean University Department of Harbor and River Engineering 5 Method 3: Diamond Rule Ⅳ Ⅱ Ⅲ Ⅰ ⅤⅥ Ⅶ

6. MSVLAB National Taiwan Ocean University Department of Harbor and River Engineering 6 Animation Fourier Method Image Method Diamond Rule

7. MSVLAB National Taiwan Ocean University Department of Harbor and River Engineering 7 The end Thanks for your kind attention. Your comments will be highly appreciated. Welcome to visit the web site of MSVLAB: http://ind.ntou.edu.tw/~msvlab