6. Let R= [0, L] x [0, H] × [0, K] be a rectangular in R and g(r, y) € L?([(0, L] × [0, H]). Find the series solution for the following problem: -Au = 0, IE D, u(0, y, 2) = u(L, y, z) = 0, 0 < y < H,0 < z < K, u(r, 0, 2) = u(x, H, 2) = 0, 0

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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6. Let R= [0, L] x [0, H] × [0, K] be a rectangular in R and g(r, y) € L?([(0, L] × [0, H]). Find the series solution
for the following problem:
-Au = 0,
IE D,
u(0, y, 2) = u(L, y, z) = 0,
0 < y < H,0 < z < K,
u(r, 0, 2) = u(x, H, 2) = 0,
0 <r< L,0 < z < K,
u(r, y, 0) = 0, u(r, y, K) = g(x, y),
0 < x < L,0 < y < K.
Transcribed Image Text:6. Let R= [0, L] x [0, H] × [0, K] be a rectangular in R and g(r, y) € L?([(0, L] × [0, H]). Find the series solution for the following problem: -Au = 0, IE D, u(0, y, 2) = u(L, y, z) = 0, 0 < y < H,0 < z < K, u(r, 0, 2) = u(x, H, 2) = 0, 0 <r< L,0 < z < K, u(r, y, 0) = 0, u(r, y, K) = g(x, y), 0 < x < L,0 < y < K.
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