Re: [理工] [工數] pde
※ 引述《OKOK98 (UTN)》之銘言：
: Solve the initial problem Ux+2Uy=0 ,
: U(0,y)=4e^(-2y).
有點時間沒碰一階PDE XD"
獻醜一下了
一階PDE最快的方法就先試試看d'Alembert
dx dy du
---- = ---- = ----
1 2 0
解的形式滿足u = f(v)
dx dy
┌ --- = --- y = 2x +c y-2x = c = v ,then c1 is costant
│ 1 2 1 1
│
│
│
└ du = 0 u =c2
→ 取 u = f(v) = f(y-2x) 為解
帶入題目初值
→ f(y) = 4exp[-2y]
∴f(y-2x) = 4exp[-2(y-2x)] = u
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