[分析] Poisson Equation
(Poisson Equation) Consider the Poisson problem
u_xx+u_yy=f(x,y); u(x,0)=u(0,y)=u(x,b)=u(a,y)=0
On the rectangle 0<x<a,0<y<b, where the source function f(x,y) is prescribed.
(Hint: Solve the Poisson problem by separation of variables for the case
where f(x,y)=const.=f. Notice that [(fx^2)/2] is a simple particular
solution and seek u is the form, f(x,y)=(fx^2)/2+U(x,y) , so that
u_xx+u_yy=f(x,y)+U_xx+U_yy=f(x,y) then U_xx+U_yy=0
Sol.
用分離變數法得到
U=(A+Bx)(E+Fy)+[Ccosh(kx)+Dsinh(kx)][Gcos(ky)+Hsin(ky)]
寫到這邊我都還寫得沒問題
但是下面就不知道怎麼接下去
直接用常數的方式帶好像有問題="=
不知道有沒有神人能夠幫我解這題讓我看看
還有一題
f(z)=sin(x)cosh(y)+i*cos(x)sinh(y)
求f'(z)
我是代
f(z)=-cos(x)sin(y)+i*sin(x)cos(y)
u=-cos(x)sin(y)
v=six(x)cos(y)
但是這樣算出來是錯的
我用wolframe跑的結果我不是很懂
有請神人幫我解釋一下
謝謝
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※ 編輯: Yenglin 來自: 1.169.173.15 (06/11 11:06)