Re: [Help-gsl] references for rk4imp and gear2 in version 1.13

[Tuomo Keskitalo]

Hello all,

please be aware that some of the old implicit methods in old ode-initval 
(like rk4imp and gear2) used a fixed number of internal functional 
iterations to get a result. There is no check for convergence of the 
iterative solution, so it is possible that your results may be partially 
erraneous. I suggest that you try to run some validation runs with a few 
other methods. If you get same results, then your old results should be 
fine. In future, I suggest you use ode-initval2.

BR,
Tuomo

On 10.12.2017 21:24, Halasz Gabor wrote:
> Dear Mohammad,
>
> Thank you for your answer.
>
> You are right. But at the moment I have all the results I need for publication. 
> We are writing the paper and I think it would be awful to repeat the hole 
> --otherwise correct-- calculations in this phase of our work just because there 
> is a newer version of a software around.
>
> Best regards,
> Gábor
>
> On 2017. december 10. 20:05:25 Mohammad Akhlaghi wrote:
> > Dear Gábor,
> >
> > You don't need root access to build and install a different version of GSL (or 
> > any software) on a server. A complete description of how to do it is given here:
> >
> > https://www.gnu.org/software/gnuastro/manual/html_node/Installation-directory.html
> >
> > Following the names in that page, to compile your own programs with your GSL 
> > installation (not the server's), just add these two options to your compilation 
> > command (they are described in that page).
> >
> > -I/YOUR-HOME-DIR/.local/include
> > -L/YOUR-HOME-DIR/.local/lib
> >
> > Cheers,
> > Mohammad
> >
> > On December 10, 2017 7:34:32 PM GMT+01:00, Halasz Gabor <address@hidden> wrote:
> > > Dear Tuomo,
> > >
> > > Thank you for your answer.
> > >
> > > Actually I have found the reference for Gear's paper but never found an
> > > explanation what is the difference between  gear1 and gear2 in GSL.
> > > Actually all mentioning of Gear's method in new documents are similar
> > > to the following one:
> > > "the class of BDFs or commonly understood as Gear’s Method".
> > >
> > > But if it is a "class of methods" it would be nice if I can make it
> > > clear which variant I have used.
> > >
> > > I am using GSL on a server for which I have no root access, so I can
> > > not change the version as fast as I would like to publish our results.
> > > But despite of the old version, gear2 is an msbdf variant and bsimp is
> > > also available in this GSL version 1.13.
> > >
> > > Maybe there is a wider palette of suitable methods in the newer
> > > versions, but I am satisfied with the old version. Two of the methods
> > > provided the same results with high accuracy and these results are in
> > > agreement with the expectations.
> > >
> > > Other methods provided very similar results for a wide range of the
> > > parameters. Usually they were faster and sometimes provided results
> > > even a bit closer to the "expectations".  But they failed --including
> > > rk2imp, gear1 or bsimp-- for the cases where I needed an extreme long
> > > integration.
> > >
> > > Best regards,
> > > Gábor
> > >
> > >
> > > On 2017. december 10. 19:23:33 Tuomo Keskitalo wrote:
> > > > Hi,
> > > >
> > > > for rk4imp I suggest this reference:
> > > >
> > > > Ascher, U.M., Petzold, L.R., Computer methods for ordinary
> > > >      differential and differential-algebraic equations, SIAM,
> > > >      Philadelphia, 1998. ISBN 0898714125, 9780898714128
> > > >
> > > > I think those old Gear methods are based on this reference:
> > > >
> > > > Gear, C.W., Numerical Initial Value Problems in Ordinary Differential
> > >
> > > > Equations, 1971.
> > > >
> > > > However, I guess you really don't want to use those old deprecated
> > > > ode-initval methods. Instead, please updgrade to GSL version 2.4, use
> > >
> > > > ode-initval2, and try e.g. msbdf or bsimp methods, if your ODE system
> > > is
> > > > stiff.
> > > >
> > > > BR,
> > > > Tuomo
> > > >
> > > > On 10.12.2017 13:48, Halasz Gabor wrote:
> > > > > Hello,
> > > > >
> > > > > I have a problem with finding proper references and descriptions
> > > for some methods I have used for solving ODEs with GSL version 1.13.
> > > > > For the stepping functions gear1(2) the info page and the manuals
> > > only contain the following simple description: M=1(2) implicit Gear
> > > method.
> > > > > I am especially interested in methods rk4imp and gear2 as all the
> > > other available ones in version 1.13  was not working properly for my
> > > ODEs.
> > > > > Best regards,
> > > > > Gábor


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