Boundary-Initial Value problem

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 1YT
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Consider the Boundary-Initial Value problem
² u
du
0< x < 8,
t> 0
əx² Ət
u(0, t) = 0, u(8,t)=0, t>0
u(x,0) = x(8 — x), 0<x<8
where
This models a heated wire, with zero endpoints temperatures. The solution u(x, t) of the initial-boundary value
problem is given by the series
bn
and
Cn
8²
(2n-1) ³
5
5(2n-1)2²
9
8
ㅠ
u(x, t) = $ [ bn sin ((2n − 1) x) en
Transcribed Image Text:Consider the Boundary-Initial Value problem ² u du 0< x < 8, t> 0 əx² Ət u(0, t) = 0, u(8,t)=0, t>0 u(x,0) = x(8 — x), 0<x<8 where This models a heated wire, with zero endpoints temperatures. The solution u(x, t) of the initial-boundary value problem is given by the series bn and Cn 8² (2n-1) ³ 5 5(2n-1)2² 9 8 ㅠ u(x, t) = $ [ bn sin ((2n − 1) x) en
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