Solve Laplace's equation inside a rectangle 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need help with my Laplace's equations inside a rectangle. Part of my assignment is letters b., d., f., g., and h. I am so confused.
![EXERCISES 2.5
2.5.1. Solve Laplace's equation inside a rectangle 0 < x < L, 0 < y < H, with the fol-
lowing boundary conditions [Hint: Separate variables. If there are two homogeneous
boundary conditions in y, let u(r, y) = h(x)o(y), and if there are two homogeneous
boundary conditions in z, let u(x, y) = 0(x)h(y).]:
*(a) (0, y) = 0,
(L, y) = 0, u(x,0) = 0,
u(r, H) = f(x)
(b) (0, y) = g(y),
(L,y) = 0, u(x,0) = 0,
u(x, H) = 0
*(c) (0, y) = 0,
au
u(L, y) = 9(y), u(x,0) = 0,
u(x, H) = 0
(d) u(0, y) = g(y), u(L, y) = 0,
(r, 0) = 0,
u(x, H) = 0
*(e) u(0, y) = 0,
u(L, y) = 0,
u(x,0) – (r, 0) = 0, u(r, H) = f(x)
du
(f) u(0, y) = f(y), u(L, y) = 0,
(z,0) = 0,
(z, H) = 0
(g) (0, y) = 0,
S0 a > L/2
11 r < L/2
au
au
(L,y) = 0, u(x, 0) =
(r, H) = 0
(h) u(0, y) = 0,
u(L, y) = g(y), u(x,0) = 0,
u(x, H) = 0
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F028e02df-ce89-464d-926f-4d831e653f09%2F16a9b5ac-fa27-4f60-a3d9-f5507237042f%2Flat453q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:EXERCISES 2.5
2.5.1. Solve Laplace's equation inside a rectangle 0 < x < L, 0 < y < H, with the fol-
lowing boundary conditions [Hint: Separate variables. If there are two homogeneous
boundary conditions in y, let u(r, y) = h(x)o(y), and if there are two homogeneous
boundary conditions in z, let u(x, y) = 0(x)h(y).]:
*(a) (0, y) = 0,
(L, y) = 0, u(x,0) = 0,
u(r, H) = f(x)
(b) (0, y) = g(y),
(L,y) = 0, u(x,0) = 0,
u(x, H) = 0
*(c) (0, y) = 0,
au
u(L, y) = 9(y), u(x,0) = 0,
u(x, H) = 0
(d) u(0, y) = g(y), u(L, y) = 0,
(r, 0) = 0,
u(x, H) = 0
*(e) u(0, y) = 0,
u(L, y) = 0,
u(x,0) – (r, 0) = 0, u(r, H) = f(x)
du
(f) u(0, y) = f(y), u(L, y) = 0,
(z,0) = 0,
(z, H) = 0
(g) (0, y) = 0,
S0 a > L/2
11 r < L/2
au
au
(L,y) = 0, u(x, 0) =
(r, H) = 0
(h) u(0, y) = 0,
u(L, y) = g(y), u(x,0) = 0,
u(x, H) = 0
%3D
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