Re: [理工] [工數] PDE
※ 引述《a149851571 (yem)》之銘言：
: http://rapid.lib.ncu.edu.tw:8080/cexamn/tai/ecy100.PDF
: 請問第六題PDE怎麼解呢？
: 半無限區域是不是適合用拉式做？
: 但是我做到一半有e^(s^2)的項使我難以繼續
: 各位高手可以幫忙給一點提示嗎？感謝
對x取Laplace
2
d U(x,t)
________ = 3[sU-f(0,t)] f(0,t)=4cos(πt)
2
dt
解ODE
12cos(πt)
U(s,t) = c1cosh(3st^2)^0.5 + c2sinh(3st^2)^0.5 + _________
2
π +3s
代入 f't(x,0) = f't(x,10) = 0
得c1=c2=0
12cos(πt) -1
U(s,t) = _________ 取L[U(s,t)]
2
π +3s
-(xπ^2)/3
U(x,t) = 4* e * cos(πt) #
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 59.126.9.183
推
01/28 23:41, , 1F
01/28 23:41, 1F
※ 編輯: pseudosula 來自: 59.126.9.183 (01/28 23:44)
→
01/28 23:45, , 2F
01/28 23:45, 2F
→
01/28 23:50, , 3F
01/28 23:50, 3F
→
01/28 23:50, , 4F
01/28 23:50, 4F
推
01/29 00:10, , 5F
01/29 00:10, 5F
→
01/29 00:14, , 6F
01/29 00:14, 6F
→
01/29 01:10, , 7F
01/29 01:10, 7F
推
01/29 01:16, , 8F
01/29 01:16, 8F
→
01/29 01:17, , 9F
01/29 01:17, 9F
※ 編輯: pseudosula 來自: 59.126.9.183 (01/29 08:57)
→
01/29 08:57, , 10F
01/29 08:57, 10F
→
09/11 14:49, , 11F
09/11 14:49, 11F
討論串 (同標題文章)