| Re: How Accurate is Runge-Kutta? |
|
 |
|
 |
|
 |
|
 |
Group: comp.lang.fortran · Group Profile
Author: C6L1VC6L1V Date: Apr 27, 2007 09:33
On Apr 26, 2:54 pm, Matt hotmail.com> wrote:> Hello. I'm currently investigating some strange results I'm getting in
> a simulation using the fourth Order Runge-Kutta algorithm. Basically
> I'm quite certain that the numerical method is to blame for some
> slightly errornous results cropping up in the more extreme regions of
> my simulation. However, I have just tried halving the stepsize used,
> and it made no difference.
>
> Is it possible that there are inhenrent inaccuracies in the Fourth
> Order Runge-Kutta method that no matter how low the stepsize goes,
> they will always be there?
If your system of DE's is "stiff", you may need to go with another
type of integrator, such as one of the predictor-corrector methods.
Runge-Kutta simply does not always work. There are whole research
groups in places like Electrical Engineering or Physics departments
who work, even today, at developing better numerical DE solvers, and
they do so because they have to: for many circuit-design or power
system problems, classical methods like Runge-Kutta are just not good
enough.
Choosing a best step-size can be a non-trivial problem: if it is too
large, truncation errors are excessive, but if it is too small,
roundoff errors ruin everything. If you want really small step-sizes,
you may need to go with extended-precision arithmetic. Most numerical
analysis books or books about the numerical solution of DEs will
contain discussions of stepsize choice.
Good luck.
R.G. Vickson
>
> Kind Regards,
>
> Matt
| 
