计算热传导方程的精确特征模式
指定一个齐次狄利克雷边界条件下的热传导方程.
In[1]:=

{\[ScriptCapitalL], \[ScriptCapitalB]} = {D[u[t, x], t] ==
Laplacian[u[t, x], {x}], DirichletCondition[u[t, x] == 0, True]};
求最小的四个特征值和特征函数.
In[2]:=

{vals, funs} =
DEigensystem[{\[ScriptCapitalL], \[ScriptCapitalB]}, u[t, x],
t, {x, 0, \[Pi]}, 4]
Out[2]=

可视化特征函数.
In[3]:=

Table[Plot3D[funs[[i]] // Evaluate, {x, -3, 3}, {t, 0, 1/3},
PlotRange -> All, Ticks -> False, Mesh -> False], {i, 4}]
Out[3]=
