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I am trying to solve this pde numerically with Mathematica:

Needs["NDSolve`FEM`"]
NDSolve[{2 f[x, y] + I*D[f[x, y], y, y] - I*D[f[x, y], x, x] - 
2 x*D[f[x, y], y] + 2 x*D[f[x, y], x] + 2 y*D[f[x, y], y] - 
2 y*D[f[x, y], x] + 2*f[x, y]*x^2 - 4 f[x, y]*x*y + 
2*f[x, y]*y^2 - 2 I*x*D[f[x, y], y] - 2 I*x*D[f[x, y], x] + 
2 I*y*D[f[x, y], y] + 2 I*y*D[f[x, y], x] == 0, 
f[x, 0] == Exp[-x], f[x, 1] == 1}, f, {x, 0, 1}, {y, 0, 1}]

However, even if I chop of parts of my equation to make it easier to solve, I keep getting the error message:

 NDSolve::femdpop: The FEMStiffnessElements operator failed.

What does this mean? I've found this post here, but I have not found the meaning of my error message.

As a side note, I am using Mathematica 10.

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  • $\begingroup$ may be it does not like the complex part. (all those I's in there). Is this quantum mechanics problem? No beep sound is generated when the "I's" are removed. $\endgroup$ – Nasser Mar 30 '15 at 4:50
  • $\begingroup$ This means that the FEM had an issue with discretizing the PDE. I filed this as a bug but as @Nasser suggests it seems to have something to do with complex values. $\endgroup$ – user21 Mar 30 '15 at 7:40
  • $\begingroup$ @Nasser Yes, this is a quantum mechanics problems. I'm trying to solve the equation for quantum Brownian motion numerically, with all constants set to 1 and by assuming that the solution is separable. $\endgroup$ – user85503 Mar 31 '15 at 2:13
  • $\begingroup$ Since FEM is unable to discretize the PDE, is there any method which will solve the differential equation? $\endgroup$ – user85503 Mar 31 '15 at 2:16
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This bug has been fixed as of Mathematica 10.4.0.

enter image description here

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