Re: [Bug-gsl] [bug #30540] please, add convergence checks in rk4imp/rk2imp

[Tuomo Keskitalo]

Hi,

On 09/02/2010 02:26 PM, Sergey B Kirpichev wrote:

> Right.  Fixed version (with jacobian, attached below) seems to be working.
>
> Actually, it works only for eps_abs ~ round off error.  Already for
> eps_abs = 1e-10 it's easy to see small (linear?) drift in hamiltonian
> from the constant.

Sorry, I'm not familiar with your problem. Can you please elaborate?

> Why mix step size control tolerances and root-finding tolerances?
>
> Why not just use prefered fixed value of eps_abs for root-finding
> (e.g.: GSL_DBL_EPSILON), as does attached patch for bug #30540 or
> other implicit solvers (e.g.
> http://www.unige.ch/~hairer/prog/stiff/radau5.f), but instead
> complicate low level solver routines?

I think both tolerances are related to the user's "desired error level", 
so it makes sense to use the same information for stopping both Newton 
iteration and adjusting the step size. If only 10^-8 solution is wanted, 
then it is not necessary to make Newton iteration until precision of 
10^-16 is reached.

Can you please point me the source code line in radau5.f in question? 
Thanks!

BR,
Tuomo

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