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Solving this "simple" PDE

  1. Jan 21, 2016 #1
    Hi guys,

    I've distilled the 3D Diffusion Equation into the following PDE using Fourier spectral techniques:

    ∂C(m,n,p,t)/∂t + k(p^2+m^2+n^2)C(m,n,p,t)=0,

    where C is the Fourier coefficient of the 3D Fourier transform, {m,n,p} are the spatial frequencies, and t is time. I've tried using a simple explicit scheme:

    C(m,n,p)v+1=1/(1+k*deltaT*(p^2+m^2+n^2)*C(m,n,p)v

    where v+1 is the leading time step, and v is the current time step. However, it seems to simply decay to zero over time. Any suggestions as to how I could treat it?
     
  2. jcsd
  3. Jan 21, 2016 #2

    Simon Bridge

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    Since you only care about the t dependence for the DE, this is form ##\frac{dy}{dt} + ay = 0## which can be solved exactly.
     
  4. Jan 22, 2016 #3
    Thanks!
     
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