# Kernel crashes when computing finite difference mixed derivative with respect to y & z but works fine when computing with respect to x & y or x & z?

Bug introduced in 8.0.4 or earlier, fixed in 11.0.0.

I am using Mathematica 10.4.0 on Ubuntu 16.04.

I am trying to solve a set of differential equations using finite difference method on an NxNxN cubic grid (x, y, z directions). I am getting a weird kernel crash when I am using NDSolveFiniteDifferenceDerivative. My code is below. The code works fine when computing mixed derivatives with respect to x&y or x&z (MXwx110 and MXwx101), but the kernel crashes every time I compute mixed derivatives with respect to y&z. I do not understand what is wrong. This is really weird.The whole thing was running perfectly fine before I had inserted boundary conditions (BCwx1) in the definition of the grid (Wx1) to make the code faster. I would really appreciate any help to resolve this issue. Thank you.

NN = 20; RMax = 20.0; delta = 1.0/NN;
xgrid = RMax*N[delta* Range[0, NN]];
ygrid = RMax*N[delta* Range[0, NN]]; zgrid = RMax*N[delta* Range[0, NN]];
fdd[l_, m_, n_] := NDSolveFiniteDifferenceDerivative[Derivative[l, m, n], {xgrid, ygrid, zgrid},"DifferenceOrder" -> {4, 4, 4}];

BCwx1 = Flatten[{Table[{Subscript[wx1, 0, j, k] -> 0.0}, {j, 0, NN}, {k, 0, NN}],
Table[{Subscript[wx1, i, 0, k] -> 0.0}, {i, 0, NN}, {k, 0, NN}],
Table[{Subscript[wx1, i, j, 0] -> 0.0}, {i, 0, NN}, {j, 0, NN}],
Table[{Subscript[wx1, NN, j, k] -> 0.0}, {j, 0, NN}, {k, 0, NN}],
Table[{Subscript[wx1, i, NN, k] -> 0.0}, {i, 0, NN}, {k, 0, NN}],
Table[{Subscript[wx1, i, j, NN] -> 0.0}, {i, 0, NN}, {j, 0, NN}]},3];

Wx1 = Table[Subscript[wx1, i, j, k] /. BCwx1, {i, 0, NN}, {j, 0, NN}, {k, 0,NN}];

MXwx110 = D[Subscript[A, 1, 1][x, y, z], {x, 1}, {y, 1}, {z, 0}] -> fdd[1,1,0][Wx1] /. BCwx1;

MXwx011 = D[Subscript[A, 1, 1][x, y, z], {x, 0}, {y, 1}, {z, 1}] -> fdd[0,1,1][Wx1] /. BCwx1;

MXwx101 = D[Subscript[A, 1, 1][x, y, z], {x, 1}, {y, 0}, {z, 1}] -> fdd[1,0,1][Wx1] /. BCwx1;

• Try not to use Subscript. It causes many problems... Commented Apr 26, 2016 at 1:24
• Sure, I can try that. I have now localized the issue the definition MXwx011. I do not think the issue is really with the subscript....it would create problems my other two definitions otherwise as well. This is why I am finding it really weird ! Commented Apr 26, 2016 at 1:33
• Also, I copied the code from my mathematica notebook....Which is why you are seeing the subscript function explicitly. Commented Apr 26, 2016 at 1:38
• fdd[0,1,1][Wx1] is causing the problem, and it is bizarre that all other possible combination of inputs (like fdd[0,0,1][Wx1]) work as intended... Commented Apr 26, 2016 at 2:37
• Exactly. I narrowed down the error to fdd[0,1,1] as well. But I have no idea why this is happening even though my system is full symmetric (it is a cube). Commented Apr 26, 2016 at 3:42