求某个区间内的特征值
指定区域.
In[1]:=
![Click for copyable input](assets.zh/find-eigenvalues-that-lie-in-an-interval/In_56.png)
\[CapitalOmega] =
ImplicitRegion[(x^2 + y^2 + 2 y)^2 < 4 (x^2 + y^2), {x, y}];
设定拉普拉斯算子.
In[2]:=
![Click for copyable input](assets.zh/find-eigenvalues-that-lie-in-an-interval/In_57.png)
\[ScriptCapitalL] = -Laplacian[u[x, y], {x, y}];
设定狄利克雷边界条件.
In[3]:=
![Click for copyable input](assets.zh/find-eigenvalues-that-lie-in-an-interval/In_58.png)
\[ScriptCapitalB] = DirichletCondition[u[x, y] == 0, True];
用细化网格求特定区间上的特征值和相应的特征函数.
In[4]:=
![Click for copyable input](assets.zh/find-eigenvalues-that-lie-in-an-interval/In_59.png)
{vals, funs} =
NDEigensystem[{\[ScriptCapitalL], \[ScriptCapitalB]},
u, {x, y} \[Element] \[CapitalOmega], 1,
Method -> {"Eigensystem" -> {"FEAST", "Interval" -> {400, 405}},
"SpatialDiscretization" -> {"FiniteElement",
"MeshOptions" -> {"MaxCellMeasure" -> 0.001}}}]
Out[4]=
![](assets.zh/find-eigenvalues-that-lie-in-an-interval/O_26.png)
可视化求得的特征函数.
显示完整的 Wolfram 语言输入
Out[5]=
![](assets.zh/find-eigenvalues-that-lie-in-an-interval/O_27.png)