(adsbygoogle = window.adsbygoogle || []).push({}); 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))

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# Homework Help: PDE problem

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