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Solving Steady Fokker-Planck Equation in 2D using standard software

  1. Aug 21, 2012 #1
    Hello all,

    I am trying to solve the FPE in 2D,

    The equation is (with implied summation over repeated indices):

    [itex] 0 = \left(- \displaystyle \frac{d}{dx_i} D_i^{(1)} + \frac{d}{dx_i}\frac{d}{dx_j} D_{ij}^{(2)}\right) ( n ) [/itex]

    where my diffusion coefficients (the D are functions of position; i.e they may not be constants. I don't have them analytically, but I have another microscopic model that calculates these diffusion coefficients and gives them to me in a discrete array. These are smooth functions in general, therefore I can interpolate them if I need to give "continuous" descriptions of them.

    I am trying to crack pdetool Box from MATLAB; but I am having trouble whether the FPE fits into an "elliptic" function category; or would I ever be able to put Drift and Diffusion coefficients that are changing in position?

    I attend a public university, and I have access to standard software such as Mathematica, Matlab, Maple, Comsol or any other that comes to mind. Does anyone have experience with a problem like this?

    Any help would be greatly appreciated.

  2. jcsd
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