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!

Diffusion Equation by Method of Images

  1. Mar 27, 2009 #1
    1. The problem statement, all variables and given/known data
    I need help in solving a problem I was assigned from Numerical Methods for Physics, 2nd Ed., by Garcia. We are asked to create a solution, by hand, for the diffusion equation, using the method of images. In particular, we have a 1-dimensional bar, centered at x = 0, of length = L. Our initial condition is a Dirac delta heat source at x = L/4. We have Neumann boundary conditions (the spatial derivatives of the temperature at the ends of the bar are zero).


    2. Relevant equations
    We know that the Gaussian is a solution, so we use Gaussians in our method of images.


    3. The attempt at a solution
    I was able to solve the situation for a Dirac delta heat source at x = 0. Basically, I drew a picture of the spatial derivative of the Gaussian, centered at x = 0. For the Neumann boundary conditions, I know that I just add identical images of the original Gaussian at increments of nL (n being an index). However, for the case where the Gaussian is centered at x = L/4, I am having trouble creating a series solution using the method of images. I've tried several variations of pictures (derivatives of Gaussians along an x-axis), but none of them give me the spatial derivative to be zero at the end points (x = +-L/2). I would greatly appreciate any help on this problem.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Diffusion Equation by Method of Images
  1. Method of images (Replies: 0)

  2. Help with Diffusion (Replies: 0)

  3. Diffusion vs. size (Replies: 0)

Loading...