Consider the Boundary-Initial Value problem where bn = and 8²u u 0 0 8.x² It u(6, 1) = 0, t>0 u(0, t) = 0, u(x,0) = x(6x), 0
Consider the Boundary-Initial Value problem where bn = and 8²u u 0 0 8.x² It u(6, 1) = 0, t>0 u(0, t) = 0, u(x,0) = x(6x), 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the Boundary-Initial Value problem
where
bn =
and
3
C₂ =
8²u Ou
8.x² It
0<x<6, t> 0
u(0, t) = 0,
u(6, 1) = 0, t>0
u(x,0) = x(6x), 0<x<6
This models a heated wire, with zero endpoints temperatures. The solution z(x, t) of the initial-boundary value problem is given by the series
b₁, sin((2n-1))
=
u(x, t) =
8
Σb,
n=1
e
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