Problem in Fourier series and Pdes

Discussion in 'Undergraduate Math' started by junoexpress, Nov 11, 2011.

  1. junoexpress

    junoexpress Guest

    Hi,

    I am working on a problem from Churchill and Brown "Fourier series and
    PDEs", 7th ed.

    Problem is to solve the heat eqn:
    (i) U_t = k * U_x,x -inf<x<+inf, t>0

    Given the initial temp distbn:
    f(x) = 1 if x>0, 0 if x<0

    I work through the problem and get the soln:
    U(x,t) = 1/2 * (1 - Erf[ x / (2*sqrt(k*t)] ) for t>0
    the book gets the same soln but has a plus sign between the two terms.

    Does anyone know offhand which soln is correct or if the book is in
    error on this problem. I've gone through it several times and cannot
    find an error on my part.

    Thanks,
    Matt
     
    junoexpress, Nov 11, 2011
    #1
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  2. The easiest thing is to consider the limit of U(x,t) as t->0.
    Remember Erf[x]->1 as x->oo, and -1 as x->-oo. It looks to me like
    Churchill and Brown are correct, and you are incorrect.
     
    Stephen Montgomery-Smith, Nov 12, 2011
    #2
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  3. junoexpress

    biofilm Guest

    what does the effect of + or a - have ? increases or decreases?
     
    biofilm, Nov 12, 2011
    #3
  4. junoexpress

    biofilm Guest

    what is min and max value of the + or the - and does that make sense ?
     
    biofilm, Nov 12, 2011
    #4
  5. junoexpress

    junoexpress Guest

    Yes, that makes sense. Thank you for the observation ;>)
     
    junoexpress, Nov 12, 2011
    #5
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