Consider the Boundary-Initial Value problem 8² u du 0< x < 8, t> 0 მx2 Ət u(0, t) = 0, u(8,t) = 0, t>0 u(x, 0) = x(8 - x), 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 5T
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Consider the Boundary-Initial Value problem
where
bn:
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
=
and
Cn
J²u
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
8²
(2n-1) ³
5
"
u(x, t) = $ [ bn
n=1
((2n-1)x) e
sin ((2n
e-cnt
Transcribed Image Text:Consider the Boundary-Initial Value problem where bn: 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 = and Cn J²u 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 8² (2n-1) ³ 5 " u(x, t) = $ [ bn n=1 ((2n-1)x) e sin ((2n e-cnt
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