Hello Jean,
It will work for me.

I think you should use the last point in the results (N+1, n+1 rows). There is no point in increasing to much the number of steps. Moreover, increasing N for Rkadapt() will cause its failing (The maximum number of iterations is exceeded). For dn_GearsBDG() will do do job but the number of steps will not change the final results (only the calculation time will increase by increasing n)
Regards,
Radovan
P.S
Hmm...I can not remember if there is a possibility to change the accuracy of these algorithms

.
EDIT: Ah yes, by setting the variables AbsTol and RelTol (see the Martin's Reference Handbook)
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"