数学物理方程中分离变量法的MATLAB可视化
毕业论文关键词：数学物理方法 MATLAB 可视化
The visualization of the variable-separation method in mathematical physics equation by MATLAB
Abstract:
In this paper, the mathematical software MATLAB is used to realize the visualization of the variable-separation method in mathematical physics equations. The frequently used MATLAB commands as well as the procedure of variable-separation method are introduced in chapter 1 and chapter 2, respectively. In chapter 3, four kinds of eigen functions solved from one-dimension eigen-value problems are visualized; furthermore, we established the visualized results of three typical mathematical physics equations, namely wave equation, heat conduct equation and potential equation in detail. In short, we created graphs and gif animations using MATLAB for the results of the variable-separation method in mathematical physics equations. Our work provides intuitive understanding of the obscure formulas in mathematical physics, and can benefit the teaching process of variable-separation method.
Keywords: Mathematical physics equation MATLAB Visualization
目 录
绪 论 1
1 MATLAB常用命令 2
1.1简要说明 2
1.2 MATLAB常用命令 2
1.3常见问题及注意事项 6
2 分离变量法 7
2.1分离变量法简介 7
2.2分离变量法的解题步骤 7
3 分离变量法的MATLAB可视化 10
3.1一文本征值问题 10
3.1.1四种常见的本征函数系 10
3.1.2本征函数系的静态图像 11
3.2弦的本征函数的运动 12
3.2.1两端固定的弦振动 12
3.2.2左端点固定、右端点自由的弦振动 14
3.2.3两端自由的弦振动 16
3.3两端固定弦振动方程的可视化 18
3.3.1设初位移 不为零，初速度 18
3.3.2初位移 ，初速度不为零 22
3.4 热传导方程的可视化 25
3.5位势方程的可视化 27
3.5.1矩形区域位势方程 27
3.5.2 圆形区域位势方程 30
4 总结 32
致谢 33
参考文献 34
绪 论
MATLAB全称为Matrix Laboratory，解释为矩阵实验室，其主要功能有算法开发、数据分析、数据可视化。MATLAB应用十分广泛，在通信、仿真、图像处理等众多领域都能看到它的身影。
MATLAB具有良好的开放性和运行的可靠性，用法简单、适用范围广、程序结构强，尤其在数值计算方面占有很重要的地位。MATLAB的主要特点有：（1）计算功能强大；（2）绘图方便；（3）功能强大的工具箱；（4）完整的帮助功能；（5）用户界面友好；（6）交互性强。