One-Dimensional Heat Equation Problem

  • Thread starter HansLee
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  • #1
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Hi, I need help to solve this problem, about 1-D heat equation

[tex]\partial[/tex]u / [tex]\partial[/tex]t = k ([tex]\partial[/tex]2u / [tex]\partial[/tex]x2)-2u (0< x <1)

u(x,0)=e-x
u(0,t)=e-2t
u(1,t)=0

I need to solve it with separation variable
 

Answers and Replies

  • #2
Office_Shredder
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Ok... what have you done so far? Do you know how to start a problem like this?
 
  • #3
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No, I have no idea how to start it, bcos it's non-homogeneous eq, can u help me?
 
  • #4
Office_Shredder
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I just realized that you don't actually have the heat equation in your first post. There should be no -2u term in the equation. Can you verify what you're supposed to be solving?

If you're actually trying to solve the heat equation, then start with u(x,t) = X(x)T(t) for some X and T functions and then try to separate the x's and the t's
 
  • #5
HallsofIvy
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Even with the "-2u" term, do exactly what Office Shredder says, just what you would normally do to "separate variables"- let u(x,t)= X(x)T(t) and put into the equation:

[tex]X\frac{du}{dt}= \kappa T\frac{d^2X}{dx^2}- 2XT[/tex]

divided through by XT and see what happens.
 

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