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!

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


    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)


    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: What is going on here? (Heat equation w/ Neumann conditions)