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Differential Equations by Pearson
book

Differential Equations by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
472 pages
13h 25m
English
Pearson India
Content preview from Differential Equations by Pearson
Partial Diff erential Equations 8-93
Now applying boundary condition (8.538):
0
1
(,0) sin
n
n
ux d nx u
=
==
(8.542)
Equation (8.542) is a half-range Fourier sine series expansion for u
0
in
(0, p) and hence the Fourier constants d
n
are given by
0
0
0
0
0
2
2cos
sin
0 if is even
2
(cos 1)
4
if is odd.
n
u
nx
d u nx dx
n
n
u
n
u
n
n
n
0
⎛⎞
==
⎜⎟
⎝⎠
=−=
p
p
pp
p
p
p
(8.543)
No
w (8.541) reduces to
0
1,3,5
4
(,) sin
ny
n
u
uxy nxe
n
=
=
p
(8.544)
which is the required solution.
Example 8.13.21 The temperature u (x, y) is maintained at 0°C
along three edges of a square plate of side 100 cm and the four
th edge
is maintained at a constant temperature u
0
until steady-state conditons
pre ...
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Publisher Resources

ISBN: 9781299487406Publisher Website