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

[Sergey B Kirpichev]

URL:
  <http://savannah.gnu.org/bugs/?30540>

                 Summary: please, add convergence checks in rk4imp/rk2imp
                 Project: GNU Scientific Library
            Submitted by: skirpichev
            Submitted on: Сбт 24 Июл 2010 12:15:06
                Category: Accuracy problem
                Severity: 3 - Normal
        Operating System: 
                  Status: None
             Assigned to: None
             Open/Closed: Open
                 Release: 
         Discussion Lock: Any

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Details:

Quote from http://lists.gnu.org/archive/html/help-gsl/2009-12/msg00047.html

--->8---
It seems, for example, the 2 stages Gauss points are only iterate 3 steps,
without checking whether it is converged or not.

The reason I care about this is, Implicit Gauss RK4 is symplectic, which for
Hamiltonian Dynamics simulation is a very important property, it has better
conservation of the first integral.
--->8---

Attached example code (bug.c) for Henon-Heiles problem shows the linear error
grow in the Hamiltonian.  Compare with correct behavior for patched solvers
(rk2imp.png/rk4imp.png).

Please, review attached patch, targeted to solve the problem.




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File Attachments:


-------------------------------------------------------
Date: Сбт 24 Июл 2010 12:15:06  Name: bug.c  Size: 2kB   By: skirpichev

<http://savannah.gnu.org/bugs/download.php?file_id=21050>
-------------------------------------------------------
Date: Сбт 24 Июл 2010 12:15:06  Name: rk2imp.png  Size: 16kB   By:
skirpichev

<http://savannah.gnu.org/bugs/download.php?file_id=21051>
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Date: Сбт 24 Июл 2010 12:15:06  Name: rk4imp.png  Size: 13kB   By:
skirpichev

<http://savannah.gnu.org/bugs/download.php?file_id=21052>
-------------------------------------------------------
Date: Сбт 24 Июл 2010 12:15:06  Name:
0001-Add-convergence-checks-for-rk-imp.patch  Size: 9kB   By: skirpichev

<http://savannah.gnu.org/bugs/download.php?file_id=21053>

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