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AW: NDSolve with a InterpolationFunction, Mathematica 5.0

  • To: mathgroup at smc.vnet.net
  • Subject: [mg43118] AW: NDSolve with a InterpolationFunction, Mathematica 5.0
  • From: Klamser at t-online.de (Peter Klamser)
  • Date: Wed, 13 Aug 2003 07:49:50 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,
I have a 4-D data field w:{{x1,y1,z1,g1}..}
W = Interpolation[WData] -> InterpolatingFunction[{{-1000., 1000.}, {-1000.,
1000.}, {-1300., 150.}}, <>]
Remark: W[[1, 1, 1]] returns -1000
Solving a ODE with NDSolve works fine:
uv=u/.NDSolve[{Derivative[1][u][x]\[Equal]
            Sign[Derivative[1,0,0][W][x,-900,
                  0]](1-1/(Sqrt[1+Derivative[1,0,0][W][x,-900,0]^2])),
          u[-900]\[Equal]0},u,{x,-900,900}]//First
uv[1] -> \!\(\(-2.5497455527383703`*^-10\)\)
Now comes the problem:
I want to have a general function for all the three directions x, y and z as
follows:
u /. NDSolve[{Derivative[1, 0, 0][u][x, y, z] ==
Sign[Derivative[1, 0, 0][W][x, y, z]](1 -
1/(Sqrt[(1 + (Derivative[1, 0, 0][W][x, y, z])^2)])),
u[W[[1, 1, 1]], y, z] == 0},
u, {x, W[[1, 1, 1]], W[[1, 1, 2]]}, {y, W[[1, 2, 1]], W[[1, 2, 2]]}, {z,
W[[1, 3, 1]], W[[1, 3, 2]]}] // First
It looks so, that Mathematica 5.0 dislikes NDSolve problems in three
dimensions.
And Mathematica 5.0 says, it can't find w[[1,1,1]] an forgets the definition
if W as a InterpolatingFunction.
Regards
Peter Klamser

[Contact the author to get WData - moderator]


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