1. 解Laplace方程式
1 1
u + ---u + --- u = 0, 0<=r<2, -π<=θ<=π
rr r r r^2 θθ
u(2,θ)=|θ|, -π<=θ<=π
2. 解Poisson方程式
2
u + u = π sinπx 0<x<1, 0<y<2
xx yy
u(0.y) = u(1,y) = 0, 0<y<2
u(x,0) = 2sin3πx, u(x,2) = -sinπx
3. 解單位圓盤Poisson方程式
1 1
u + ---u + --- u = 9r + 6cosθ + 3sinθ, 0<r<1.
rr r r r^2 θθ
u(1,θ) = 1 - 3sinθ -π<θ<π
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