Solve the Boundary-Initial Value Problem where a = k n21 8²u du dz² Ət " du ax (0, 1) = 0, 0 0 du Oz (L,t)=0, t>0 that models the temperature of a heated wire with insulated ends. The series solution of the boundary value problem is u(s, t) = ²a,e(-¹) cos (17) u(a,0)=x², 0<#

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Solve the Boundary-Initial Value Problem
2²u
du
əx² It'
where a =
k
n21
du
da
du
?х
u(a,0)=x², 0<x<L
(0, t) = 0,
that models the temperature of a heated wire with insulated ends. The series solution of the boundary
value problem is
0<x<L, t>0
m=0
(L,t)=0, t>0
u(x, t) = ²a,e(-²1)
&(r,
Remember that has already been factored out!
cos
(1 x)
Transcribed Image Text:Solve the Boundary-Initial Value Problem 2²u du əx² It' where a = k n21 du da du ?х u(a,0)=x², 0<x<L (0, t) = 0, that models the temperature of a heated wire with insulated ends. The series solution of the boundary value problem is 0<x<L, t>0 m=0 (L,t)=0, t>0 u(x, t) = ²a,e(-²1) &(r, Remember that has already been factored out! cos (1 x)
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