Solve Laplace's equation, a2u azu = 0,0 < x < a, 0 < y < b, (see (1) in Section 12.5) for a rectangular plate subject to the given boundary condition əy? u(0, y) = 0, du u(1, у) = 0 %3D и(x, 0), u(x, 1) = f(x) %3D ây ly = 0 NITX NTX 2 u(x, y) = 2 sinh sin where An + f(x) sin(ntx) dx 'n NIt cosh(nt) + sinh(nn) Jo a a n = 1
Solve Laplace's equation, a2u azu = 0,0 < x < a, 0 < y < b, (see (1) in Section 12.5) for a rectangular plate subject to the given boundary condition əy? u(0, y) = 0, du u(1, у) = 0 %3D и(x, 0), u(x, 1) = f(x) %3D ây ly = 0 NITX NTX 2 u(x, y) = 2 sinh sin where An + f(x) sin(ntx) dx 'n NIt cosh(nt) + sinh(nn) Jo a a n = 1
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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Please solve using simple logical steps and have final answer in correct format.
Transcribed Image Text:Solve Laplace's equation,
a2u
azu
= 0,0 < x < a, 0 < y < b, (see (1) in Section 12.5) for a rectangular plate subject to the given boundary condition
əy?
u(0, y) = 0,
du
u(1, у)
= 0
%3D и(x, 0),
u(x, 1) = f(x)
%3D
ây ly = 0
NITX
NTX
2
u(x, y) =
2 sinh
sin
where An
+
f(x) sin(ntx) dx
'n
NIt cosh(nt) + sinh(nn) Jo
a
a
n = 1
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