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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
Partial Differential Equations 12-31
3
333 33
22 8
0 0 (( 1) 1) , ( : odd ).
n
l
n
ln n
aa
pp
⎡⎤
=+− −−=
⎢⎥
⎣⎦
Hence the temperature distribution in the bar is
given by
33
1
2
22
2
(2 1)
81
(,) sin
(2 1)
(2 1)
exp
n
nx
uxt
l
n
n
at
l
p
a
p
p
=
=
⎛⎞
⎜⎟
⎝⎠
Example 12.60
Find the temperature in a thin metal rod of length l
with both ends insulated and with initial tempera-
ture in the rod sin (p x/l ).
Solution The initial boundary value problem
consists of the following
1. Partial differential equation for conduction of heat
2
2
2
uu
a
t
x
∂∂
=
(1)
2. Boundary conditions: (Insulation at both ends)
0
0;
x
u
x
=
=
0
xl
u
x
=
=
(2), (3)
3. Initial condition:
(,0) sin
x
ux
l
⎛⎞
=
⎜⎟
⎝⎠
p
(4)
The general solution ...
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Publisher Resources

ISBN: 9781299446557Publisher Website