4. u(0, 1) = 0, u(π, t) = 0, t>0 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Answer question 4
![In Problems 1-6, solve the heat equation (1) subject to the
given
conditions.
1. u(0, t) = 0, u(L, t) = 0, t> 0
u(x,0)= 100, 0<x<L
2 u(0, 1) = 0, u(L, t) = 0, t> 0
u(x,0) = x(L-x), 0<x<L
5.
6.
au
axx-o
ax=L
u(x, 0) = f(x), 0 < x < L
dul
ди
x=0
= 0,
= 0,
u(x, 0) =
axx-2
= 0, 1>0
= 0, 1>0
[x,
0<x<1
(0, 1<x<2
3. u(0, t) = 0, u(L, 1) = 0, t> 0
0<x<L/2
L/2<x<L
u(π, t) = 0, t> 0
u(x, 0) =
4. u(0, 1) = 0,
u(x, 0)
(1,
10,
=
(T-X,
-x,
0<x< π/2
π/2<x< T
13.3 Heat Equation 727
a²u
ди
ax²
at
u(-L, t) = u(L, 1), 1>0
ди
-L<x<L, 1>0,
ди
ax
|x=-L
u(x, t) = f(x), -L<x<L.
=
, 1>0
axx=L
See (15) in Section 12.5. Find the temperature u(x,
Think full Fourier series 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F850c5fe0-78a8-4fb7-bf63-56ee551aa9a1%2Fde6a89d2-3546-47ec-943e-46dd39d3297d%2Fg7hqsul_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In Problems 1-6, solve the heat equation (1) subject to the
given
conditions.
1. u(0, t) = 0, u(L, t) = 0, t> 0
u(x,0)= 100, 0<x<L
2 u(0, 1) = 0, u(L, t) = 0, t> 0
u(x,0) = x(L-x), 0<x<L
5.
6.
au
axx-o
ax=L
u(x, 0) = f(x), 0 < x < L
dul
ди
x=0
= 0,
= 0,
u(x, 0) =
axx-2
= 0, 1>0
= 0, 1>0
[x,
0<x<1
(0, 1<x<2
3. u(0, t) = 0, u(L, 1) = 0, t> 0
0<x<L/2
L/2<x<L
u(π, t) = 0, t> 0
u(x, 0) =
4. u(0, 1) = 0,
u(x, 0)
(1,
10,
=
(T-X,
-x,
0<x< π/2
π/2<x< T
13.3 Heat Equation 727
a²u
ди
ax²
at
u(-L, t) = u(L, 1), 1>0
ди
-L<x<L, 1>0,
ди
ax
|x=-L
u(x, t) = f(x), -L<x<L.
=
, 1>0
axx=L
See (15) in Section 12.5. Find the temperature u(x,
Think full Fourier series 1
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