Boundary-Initial Value problem
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
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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