[ODE] Large mass and accuracy

[Ignacio.Garcia at uv.es]

Hi!

The problem you're dealing with is the solution of a 'stiff system' of
differential equations.

I quoted 'stiff system' because it is the technical term for these
kind of systems.

It is definitely not a problem of magnitude, but a problem of
ratios, as someone pointed before. Notice that if both mass and force
are large, when you divide them they give you reasonable values. There
is not high loss of accuracy. But if you have one or more very small
masses compared with the largest, the the application of the forces
that arise due to the large mass lead to numerical instability. Try to
use wheels of mass 10.000 kg for a 50.000 kg car, and youls find the
problem vanishes.

I advance that the problem is an open problem. You can find many
journal articles an PhD thesis on the subject and there is not a
'good' solution.

My advice is to add another diff. eq. solver to ODE that works better
with stiff systems. Which one? well I would first perform a search in
google, then in elsevier, acm, ieee, siam... and select a proper
method.

I'm starting some research on the subject. If things go as I expect,
in a few months I'll be able to give some technical ideas on how to
solve this problem. However I insist that it is an open problem and
what works well in some cases does not in others.

Regards.

Ignacio

-- 
May the source be with you
--------------------------------------------------------------------
Ignacio García Fernández                       Instituto de Robótica
ignacio.garcia_at_uv.es                      Universidad de Valencia
http://robotica.uv.es/~ignacio/                     Tlf. 96 354 3564