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

From: Tuomo Keskitalo
Subject: Re: [Help-gsl] references for rk4imp and gear2 in version 1.13
Date: Mon, 11 Dec 2017 18:20:32 +0200
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101 Thunderbird/52.5.0

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.


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,

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:

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).



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

Best regards,

On 2017. december 10. 19:23:33 Tuomo Keskitalo wrote:

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


On 10.12.2017 13:48, Halasz Gabor wrote:

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

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

Best regards,


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