Hello everyone! I have a problem with NDSolve. I'm trying to solve a quite complicated system of ODE (4 equations with the needf for 6 initial conditions). These are 4 Einstein's equations, second order in 2 of the 4 functions. Here is a piece of my code:
Asol[Ah0_?NumberQ, \[Phi]h0_?NumberQ, \[Chi]h0_?NumberQ] :=
A /. NDSolve[{EOM[[1]] == 0, EOM[[2]] == 0, EOM[[3]] == 0,
EOM[[4]] == 0,
A[1 - \[Epsilon]] ==
Ahor[Ah0, \[Phi]h0, \[Chi]h0][1 - \[Epsilon]],
A'[1 - \[Epsilon]] ==
Ahor[Ah0, \[Phi]h0, \[Chi]h0]'[1 - \[Epsilon]], \[Phi][
1 - \[Epsilon]] == \[Phi]hor[Ah0, \[Phi]h0, \[Chi]h0][
1 - \[Epsilon]], \[Phi]'[
1 - \[Epsilon]] == \[Phi]hor[Ah0, \[Phi]h0, \[Chi]h0]'[
1 - \[Epsilon]],
f[1 - \[Epsilon]] ==
fhor[Ah0, \[Phi]h0, \[Chi]h0][1 - \[Epsilon]], \[Chi][
1 - \[Epsilon]] == \[Chi]hor[Ah0, \[Phi]h0, \[Chi]h0][
1 - \[Epsilon]]}, {A, \[Phi], f, \[Chi]}, {z,
1 - \[Epsilon], \[Delta]}, WorkingPrecision -> 20][[1]]
Where I defined delta = 10^-8.
Now, if I call my solution as:
Asol[1, 1, 1][\[Delta]]
Then I obtain the following error message:
InterpolatingFunction::dmval: Input value {1.*10^-8} lies outside the range of data in the interpolating function. Extrapolation will be used. >>
It seems weird to me since I integrated up to delta. I also tried to ask the function at, for example, 10*delta but the same error pops up. Any idea of what I'm doing wrong?
Thanks a lot! Cheers Angelo