制約条件付きのラプラス演算子の固有値問題を解く
一次元領域上で,同次ディリクレ(Dirichlet)境界条件で制約されたラプラス方程式 の固有値と固有関数を小さい方から4個求める.
ラプラス演算子を指定する.
In[1]:=
![Click for copyable input](assets.ja/solve-the-eigenproblem-of-a-constrained-laplacian/In_4.png)
\[ScriptCapitalL] = -Laplacian[u[x], {x}];
ディリクレ境界条件を設定する.
In[2]:=
![Click for copyable input](assets.ja/solve-the-eigenproblem-of-a-constrained-laplacian/In_5.png)
\[ScriptCapitalB] = DirichletCondition[u[x] == 0, True];
固有値を数値的に求める.
In[3]:=
![Click for copyable input](assets.ja/solve-the-eigenproblem-of-a-constrained-laplacian/In_6.png)
NDEigenvalues[{\[ScriptCapitalL], \[ScriptCapitalB]},
u[x], {x, 0, \[Pi]}, 4]
Out[3]=
![](assets.ja/solve-the-eigenproblem-of-a-constrained-laplacian/O_3.png)
固有値と固有関数を数値的に求める.
In[4]:=
![Click for copyable input](assets.ja/solve-the-eigenproblem-of-a-constrained-laplacian/In_7.png)
{vals, funs} =
NDEigensystem[{\[ScriptCapitalL], \[ScriptCapitalB]},
u[x], {x, 0, \[Pi]}, 4];
固有値を調べる.
In[5]:=
![Click for copyable input](assets.ja/solve-the-eigenproblem-of-a-constrained-laplacian/In_8.png)
vals
Out[5]=
![](assets.ja/solve-the-eigenproblem-of-a-constrained-laplacian/O_4.png)
固有関数を可視化する.
In[6]:=
![Click for copyable input](assets.ja/solve-the-eigenproblem-of-a-constrained-laplacian/In_9.png)
Plot[Evaluate[funs], {x, 0, \[Pi]}]
Out[6]=
![](assets.ja/solve-the-eigenproblem-of-a-constrained-laplacian/O_5.png)