Best routine to integrate a stiff set of 10^3 ODEs

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Posted by J Hienola on February 24, 1998 at 11:10:40:

I would like to have some advices what would be a
relatively accurate and fast method to integrate
a stiff set of hundreds, even thousand, 1st order ODE's.
I have tried several different routines available on
net as a freeware and also some commercial NAG and
IMSL routines, such as semi-implicit Rosenbrock
method, and semi-implicit extrapolation method
(extremely slow), and some BDF routines (quite a fast,
commercial). Problem is that I can't calculate
Jacobian matrix of the set of my equations explicitely.
Therefore I would like to hear, if anybody knows a
good way to solve my problem. I'm using Fortran 90
language on a single processor machine, and I really
would like some uncommercial method.

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