## 数学物理方程中行波法的Matlab可视化

The visualization of the traveling wave method in Mathmatical physics equations by MATLAB
Abstract：
In this paper, the visualization of the traveling wave method in mathematical physics equations is achieved based on the matrix computation and graphic illustration of the mathematical software MATLAB. The frequently used MATLAB commands are introduced in chapter 1, and the procedure and the main conclusions of the traveling wave method for one- and three-dimension problems are introduced in chapter 2. In chapter 3, we illustrated the influence of the initial position and the initial velocity to the one-dimension string vibration, the Duhamel's principle for one-dimension inhomogeneous string vibration, and the two- and three-dimension wave propagation by graphs and gif animations using MATLAB. This paper provides intuitive understanding of the formulas in mathematical physics, and can benefit the teaching process of the traveling wave method. 源`自*六)维[论*文'网www.lwfree.cn
Keywords: MATLAB    mathematical physics equations     traveling wave method

1.MATLAB软件的简介    2
1.1 MATLAB基本介绍    2
1.2 MATLAB在数学物理方法中的应用    2
1.3 PDETOOL    3
1.4 MATLAB常用命令    3

1.5重点使用的命令    4
2.波动方程初值问题简介    6
2.1 行波法概述    6
2.2一维无界弦的波动问题    6
2.2.1 一维无界弦的自由振动问题    6
2.2.2 一维无界弦的纯受迫振动问题    8
2.2.3 一维无界弦的一般受迫振动问题    10
2.3 高维波动问题    11
2.3.1 三维波动问题的球面平均法与泊松公式    11
2.3.2 降维法与二维泊松公式    13
3.行波法的可视化    15
3.1一维无界弦的自由振动    15
3.1.1 初位移不为零，初速度为零的波动    15
3.1.2 初位移为零，初速度不为零的波动    16
3.3齐次化原理    18
3.4 二维波动方程    21
3.5 球面波问题    23

绪论

------分隔线----------------------------