拉普拉斯算子的本征值和本征函数
在一个一维区域上求解拉普拉斯算子最小的四个特征值和特征函数, 即 的解.
设定拉普拉斯算子.
In[1]:=
![Click for copyable input](assets.zh/a-laplacians-eigenvalues-and-eigenfunctions/In_1.png)
\[ScriptCapitalL] = -Laplacian[u[x], {x}];
用数值方法求最小的四个特征值和特征函数.
In[2]:=
![Click for copyable input](assets.zh/a-laplacians-eigenvalues-and-eigenfunctions/In_2.png)
NDEigensystem[\[ScriptCapitalL], u[x], {x, 0, \[Pi]}, 4]
Out[2]=
![](assets.zh/a-laplacians-eigenvalues-and-eigenfunctions/O_1.png)
可视化特征函数.
In[3]:=
![Click for copyable input](assets.zh/a-laplacians-eigenvalues-and-eigenfunctions/In_3.png)
NDEigensystem[\[ScriptCapitalL], u[x], {x, 0, \[Pi]}, 4];
Plot[Evaluate[%[[2]]], {x, 0, \[Pi]}]
Out[3]=
![](assets.zh/a-laplacians-eigenvalues-and-eigenfunctions/O_2.png)