Hi, I have a system of ODE in the form A(x).x'=F(x) (differential algebraic equations). I have solved with mathematica for an initial datum x=x1,x2. The system is invariant by exchanging x1 and x2, meaning that the solution for x=x2,x1 must be the same as for x=x1,x2. However, for x=x2,x1 I obtained an error (specifically underflow). I have checked for the construction of the matrix A(x) and it seems to be no error. I have also written a kind of RungeKutta integrator and I have the same problem (solutions appear not be invariant exchanging). I am using numeric computation maybe I did some error there.
Any idea what is going on?
If you want to have someone to look into it you should kindly consider to disclose some code, because - as Jens-Peer Kuska used to say - the magic crystal sphere standing behind me did not show it on it's own.
It could be an initialization problem, if one runs first x=x1,x2, than x=x2,x1 without clearing all variables before the second run. It could be a typo preventing the intended symmetry - did you perform successful some formal check of the intended symmetry? It could be a numeric accident, going away with bigger precision set ...