bugGNU Scientific Library - Bugs: bug #30540, please, add convergence checks in...


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bug #30540: please, add convergence checks in rk4imp/rk2imp

Submitted by:  Sergey B Kirpichev <skirpichev>
Submitted on:  Sat Jul 24 12:15:06 2010  
Category: Accuracy problemSeverity: 3 - Normal
Operating System: Status: Ready For Test
Assigned to: NoneOpen/Closed: Open

Thu Aug 26 12:05:28 2010, comment #2:

I can't figure out how to use this code for fixed step size. imprk2/imprk4 seems to be not working at all for this case:
$ ./bug
Segmentation fault

Other steppers works (e.g. rk2) just fine. See bug-ode2.c.

Second, Newton-type iterations could be inefficient in general. See: Ernst Hairer, Christian Lubich, Gerhard Wanner, Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations. Springer Series in Comput. Mathematics, Vol. 31, Springer-Verlag 2002. pp. 330-332.

(file #21314)

Sergey B Kirpichev <skirpichev>
Fri Aug 6 13:09:11 2010, comment #1:

Thanks for the bug report.

I'm merging a completely new and upgraded version of the ode solvers "ode-initval2" written by Tuomo Keskitalo in the next release. It includes the new solver ode-initval2/imprk4.c for implicit RK4.

You can get the branch with

bzr checkout http://bzr.savannah.gnu.org/r/gsl/ode-initval2/

To compile it use

autoreconf -i -f; ./configure --enable-maintainer-mode ; make

Please try it and let us know if it solves this problem.

-Deleted Account- <bjg>
Sat Jul 24 12:15:06 2010, original submission:

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

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.

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.

Sergey B Kirpichev <skirpichev>


Attached Files
file #21314:  bug-ode2.c added by skirpichev (2kB - application/octet-stream)
file #21050:  bug.c added by skirpichev (2kB - application/octet-stream)
file #21051:  rk2imp.png added by skirpichev (16kB - image/png)
file #21052:  rk4imp.png added by skirpichev (13kB - image/png)


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    Follow 6 latest changes.

    Date Changed By Updated Field Previous Value => Replaced By
    Thu Aug 26 12:05:28 2010skirpichevAttached File-=>Added bug-ode2.c, #21314
    Fri Aug 6 13:09:11 2010bjgStatusNone=>Ready For Test
    Sat Jul 24 12:15:06 2010skirpichevAttached File-=>Added bug.c, #21050
      Attached File-=>Added rk2imp.png, #21051
      Attached File-=>Added rk4imp.png, #21052
      Attached File-=>Added 0001-Add-convergence-checks-for-rk-imp.patch, #21053

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