求解基本施图姆-刘维尔问题
求解带有狄利克雷条件的特征值问题.
In[1]:=
![Click for copyable input](assets.zh/solve-a-basic-sturm-liouville-problem/In_29.png)
sol = DSolve[{y''[x] + \[Lambda] y[x] == 0, y[0] == 0, y[\[Pi]] == 0},
y[x], x]
Out[1]=
![](assets.zh/solve-a-basic-sturm-liouville-problem/O_15.png)
制作前五个特征函数的表格.
In[2]:=
![Click for copyable input](assets.zh/solve-a-basic-sturm-liouville-problem/In_30.png)
eigfuns =
Table[y[x] /.
sol[[1]] //. {\[FormalN] -> i, \[Lambda] -> \[FormalN]^2} /. {C[
1] -> 1}, {i, 5}]
Out[2]=
![](assets.zh/solve-a-basic-sturm-liouville-problem/O_16.png)
绘制这些特征函数.
In[3]:=
![Click for copyable input](assets.zh/solve-a-basic-sturm-liouville-problem/In_31.png)
Plot[Evaluate[eigfuns], {x, 0, Pi}]
Out[3]=
![](assets.zh/solve-a-basic-sturm-liouville-problem/O_17.png)
求解带有诺依曼(Neumann)条件的特征值问题.
In[4]:=
![Click for copyable input](assets.zh/solve-a-basic-sturm-liouville-problem/In_32.png)
sol = DSolve[{y''[x] + \[Lambda] y[x] == 0, y'[0] == 0,
y'[\[Pi]] == 0}, y[x], x]
Out[4]=
![](assets.zh/solve-a-basic-sturm-liouville-problem/O_18.png)
制作前五个特征函数的表格.
In[5]:=
![Click for copyable input](assets.zh/solve-a-basic-sturm-liouville-problem/In_33.png)
eigfuns =
Table[y[x] /.
sol[[1]] //. {\[FormalN] -> i, \[Lambda] -> \[FormalN]^2} /. {C[
1] -> 1}, {i, 5}]
Out[5]=
![](assets.zh/solve-a-basic-sturm-liouville-problem/O_19.png)
绘制这些特征函数.
In[6]:=
![Click for copyable input](assets.zh/solve-a-basic-sturm-liouville-problem/In_34.png)
Plot[Evaluate[eigfuns], {x, 0, Pi}]
Out[6]=
![](assets.zh/solve-a-basic-sturm-liouville-problem/O_20.png)