[其他] 分離係數法與偏微分方程
在分離係數法中
令f(x,y)=g(x)*h(y)
為何我們知道他一定可以拆這樣?
g(x)'' = d^2g(x)/dx^2
h(y)'' = d^2h(y)/dy^2
g(x)''h(y)+g(x)h(y)''=0
同除g(x)*h(y)
g(x)''/g(x)+h(y)''/h(y)=0
// 這代表說f(x,y) 不能為零 ? 但我的邊界值f(0, 0) = 0
g''/g = -a
h''/h = a
g''+ag = 0
h''-ag = 0
// 我怎知道a大於0或小於0 要把答案拆兩個部分分析?
a,b是常數 c是個變數
f(0,0)=0
f(0,a)=0
f(b,0)=0
f(a,b)=0
f(a,c)=C0 // 0<c<b
它需要用到幾個才能解出來? 全部都用到?
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