This vaguely stated question would arguably need courses in numerical analysis and numerical solutions to differential equations to answer at all well, maybe with some focus on stiff ODE systems too. Plus numerical linear algebra. Multiple books writtten, and read. I said vaguely stated, because we are not told what you are actually doing, only given a glimpse, some hints at what you are trying to do.
No, you cannot trust all 16 digits you get there, precisely because of numerical issues. The ranges of those parameters suggests you are likely far exceeding the limits of what you can compute accurately using double precision.
If you want a good answer, then make an appointment with someone with expertise on those matters. Look at your local university math department as a start, though there are some superb mathematicians residing in engineering departments too. Tell your consultant exactly what you are doing, rather than the vague glimpse you have given here.
