+) Solve Poisson problem for a=lı balруu(x₁b) = f₂(x)Du= f(x,y)u(0₁9)=9₁ (9)b0u(a.y) = 9₂ (y)>xau(x₁) = f(x)Figure 1.f(x,y) = sin2TX₁ f₁ = £₂=0, 9₁=9₂=0usingone dimensional eigen function expansion.

Use separation of variables for laplace problem then from there go to poisson problem

4) Solve Poisson problem for a=lı b=l ↑u (x₁b) = f₂(x) ty b (0₁4)=9₁(y) 0 Ou=f(x,y) u(a.y) = 9₂ (9) xx a u(x₁) = f(x) Figure 1. f(x,y) = sin2TX₁ f₁= £₂=0, 9₁=9₂=0 using one dimensional eigen function expansion. 1

4) Solve Poisson problem for a=lı b=l ↑u (x₁b) = f₂(x) ty b (0₁4)=9₁(y) 0 Ou=f(x,y) u(a.y) = 9₂ (9) xx a u(x₁) = f(x) Figure 1. f(x,y) = sin2TX₁ f₁= £₂=0, 9₁=9₂=0 using one dimensional eigen function expansion. 1

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.2: Partial Derivatives

Problem 28E

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Question

+) Solve Poisson problem for a=lı bal
ру
u(x₁b) = f₂(x)
Du= f(x,y)
u(0₁9)=9₁ (9)
b
0
u(a.y) = 9₂ (y)
>x
a
u(x₁) = f(x)
Figure 1.
f(x,y) = sin2TX₁ f₁ = £₂=0, 9₁=9₂=0
using
one dimensional eigen function expansion.

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