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Re: [Bug-gsl] [bug #30540] please, add convergence checks in rk4imp/rk2i

From: Tuomo Keskitalo
Subject: Re: [Bug-gsl] [bug #30540] please, add convergence checks in rk4imp/rk2imp
Date: Fri, 03 Sep 2010 12:18:23 +0300
User-agent: Mozilla/5.0 (X11; U; Linux x86_64; en-US; rv: Gecko/20100713 Thunderbird/3.0.6


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!



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