Solve Laplace's equation, 324 + 324 = 0 дуг u(0, y) = 0, u(a, y) = 0 ди Əy eBook ly = 0 u(x, y) = 0 = 0, 0 < x

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Solve Laplace's equation,
eBook
ди
Əy
u(x, y) = 0
u(0, y) = 0, u(a, y) = 0
a²u
ах2
y = 0
a²u
+
= 0, 0 < x <a, 0 ≤ y ≤ b, for a rectangular plate subject to the given boundary conditions
дуг
= 0, u(x, b) = f(x)
+
ΣAC
An
n = 1
DI where A,, = 2 sech (nb) f(x) sin(x) dx
An a
Transcribed Image Text:Solve Laplace's equation, eBook ди Əy u(x, y) = 0 u(0, y) = 0, u(a, y) = 0 a²u ах2 y = 0 a²u + = 0, 0 < x <a, 0 ≤ y ≤ b, for a rectangular plate subject to the given boundary conditions дуг = 0, u(x, b) = f(x) + ΣAC An n = 1 DI where A,, = 2 sech (nb) f(x) sin(x) dx An a
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