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PDE problem

  1. Feb 9, 2010 #1
    1. The problem statement, all variables and given/known data

    du/dt = (d^2)u/d(x^2), t>0, 0<x<1

    u(0,t) = 0 = u(1,t) , t>0
    u(x,0) = P(x), 0<x<1

    P(x) = {0 , if abs(x-1/2) >epsilon/2
    {u/epsilon, if abs(x-1/2) <= epsilon/2

    i need to find u(1/2,1/pi^2)

    2. Relevant equations

    i have u(x,t) = SUM{ 2/(n*pi) *P(x)*(1-cos(n*pi))sin(n*pi*x)exp(-t*(n*pi)^2)}

    3. The attempt at a solution

    so when I try to get u(1/2,1/pi^2) i get 2U/e * 2/(pi*epsilon) * (exp(-2)-exp(-10)+exp(-26)-.....)

    I know the answer is u(1/2,1/Pi^2) = 2U/e * (sin(pi*epsilon/2)/(pi*epsilon/2))
  2. jcsd
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