The boundary value problem for a heated rod with insulated ends has the formal series solution: u(x,t) =+ 2 a,exp(-n²n?kt/L²) cos- n=D1 where the {an} are the Fourier cosine series coefficients in an = S(x)cosdx for n = 0,1,2,. %3D of the rod's initial temperature function f(x) = u(x,0). %3D Use the formula above for the following boundary value problem 2u, = urx, 0
The boundary value problem for a heated rod with insulated ends has the formal series solution: u(x,t) =+ 2 a,exp(-n²n?kt/L²) cos- n=D1 where the {an} are the Fourier cosine series coefficients in an = S(x)cosdx for n = 0,1,2,. %3D of the rod's initial temperature function f(x) = u(x,0). %3D Use the formula above for the following boundary value problem 2u, = urx, 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:The boundary value problem for a heated rod with insulated ends has the formal series solution:
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u(x,t) =+ 2 anexp(-n²n²kt/L²) cos-
L
%=D1
where the {a,n} are the Fourier cosine series coefficients in
an = (x)cosdx for n = 0,1,2,.
%3D
of the rod's initial temperature function f(x) = u(x,0).
Urx, 0<x< 6,
%3D
Use the formula above for the following boundary value problem 2u,
ux(0, t) = u,(6, t) = 0, u(x, 0) = 5x
%3D
%3D
a) Calculate a,
b) Calculate an
c) Find u(x,t)
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