求解一道偏微分方程的题目
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求解一道偏微分方程的题目
U,t = U,xx (0
U,t = U,xx (0
![求解一道偏微分方程的题目](/uploads/image/z/7736687-71-7.jpg?t=%E6%B1%82%E8%A7%A3%E4%B8%80%E9%81%93%E5%81%8F%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E7%9A%84%E9%A2%98%E7%9B%AE)
设g(x,t)=G(x)T(t)
U(x,t) = g(x,t) + v(x,t)
U(1,t)=0=g(1,t)=G(1)T(t),
G(1)=0
U(x,0)=1-x=G(x)T(0)+v(x,0);G(0)+0=1-0=1;G(0)=1
U(0,t)=cos(t)=G(0)T(t)=T(t);T(0)=1
g(x,t)=G(x)T(t)=[1-x-v(x,0)]cos(t)
如果设 v(x,0)=0
g(x,t)=[1-x]cos(t)
U(x,t) = g(x,t) + v(x,t)
U(1,t)=0=g(1,t)=G(1)T(t),
G(1)=0
U(x,0)=1-x=G(x)T(0)+v(x,0);G(0)+0=1-0=1;G(0)=1
U(0,t)=cos(t)=G(0)T(t)=T(t);T(0)=1
g(x,t)=G(x)T(t)=[1-x-v(x,0)]cos(t)
如果设 v(x,0)=0
g(x,t)=[1-x]cos(t)