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!

Solving heat equation BACK in time

  1. Nov 29, 2013 #1
    I want to solve the one-dimensional heat PDE backward in time ∂u/∂t = -∇2u = -∂2u/∂x2 , x element of [0,L]

    Basically, I want to find what the initial temperature profile u(x,t=0) should be such that after some time t1 of diffusion, I am left with the bar at a uniform temperature u(x,t1)=c for c>0 and boundary conditions are convective, i.e. ∂u(L,t)/∂x = -h*u(L,t)

    I am having trouble doing this numerically using finite difference in MATLAB, and I realize this is an ill-posed problem. But it seems to be pretty simple so it should be possible. Is there some trick to solving this, or would I have to resort to a brute-force method of guess/check?

    I'd appreciate some insight. Thanks!
  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