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Homework Help: What is going on here? (Heat equation w/ Neumann conditions)

  1. Apr 20, 2012 #1
    1. The problem statement, all variables and given/known data

    Solve the heat equation

    ut=uxx

    on the interval 0 < x < 1 with no-flux boundary conditions. Use the initial condition

    u(x,0)=cos ∏x​

    2. Relevant equations

    We eventually get u(x,t)= B0 + ƩBncos(n∏x/L)exp(-n22σ2t/L2)

    where

    L=1 and σ=1 in our case.

    B0 is given by (1/L)∫[0,L]u(x,0)dx

    and Bn by (2/L)∫[0,L]u(x,0)cos(n∏x/L)dx

    3. The attempt at a solution


    Well, I keep getting Bn = (2/L)∫[0,L]u(x,0)cos(n∏x)dx = 0 after using the trig identity cos(u)cos(v)=(1/2)(cos(u+v)+cos(u-v)).

    What's happening here? I've checked my steps many times.
     
  2. jcsd
  3. Apr 20, 2012 #2
    Thoughts?
     
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