1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted