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Introductory PDE (diffusion equation)

  1. Sep 24, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]u_t = -{{u_{x}}_{x}}[/tex]
    [tex]u(x,0) = e^{-x^2}[/tex]

    2. Relevant equations



    3. The attempt at a solution
    The initial state is a bell curve centred at x=0. The second partial derivative of u at t=0 is [tex]{4x^2}{e^{-x^2}}[/tex], which is a Gaussian function, which means nothing to me other than its bell-curved shape.

    The solution is http://www.orcca.on.ca/~reid/Courses//AMath315/Fall2009/Solutions/Assign1-Fab.pdf" (the top graph), but I just want to know how on earth he (my prof who wrote up said solutions) came up that graph for time t + delta t, and what on earth he means by whatever it is he wrote down there.[tex]
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Sep 29, 2009 #2
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