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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: Sat, 04 Sep 2010 14:39:26 +0300
User-agent: Mozilla/5.0 (X11; U; Linux x86_64; en-US; rv: Gecko/20100713 Thunderbird/3.0.6

On 09/03/2010 12:35 PM, Sergey B Kirpichev wrote:
On 9/3/10, Tuomo Keskitalo<address@hidden>  wrote:
  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.

It's necessary, if you want qualitatively correct behaviour.

See, e.g.: http://www.unige.ch/~hairer/prog/gnimatlab.tar, gni_irk2.m
file (arround lines 273,289).

Thanks for the link. That is a special code meant for second order ODEs. Apparently your case requires precise solution, and therefore you should modify the Newton iteration code if you want to use GSL for your problem. However, I think your case is special. At least I do not know of a generally accepted all-purpose tolerance for the Newton iteration.

Please note that GSL ode-initval is a general-purpose ODE solver suite. The routines are not specifically meant to be suitable for the simulation of Hamiltonian mechanics. It might be best that those who need these modifications make them for their own use, unless somebody comes up with an elegant way to include this case to the framework?


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