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

[Sergey B Kirpichev]

On 8/27/10, Tuomo Keskitalo <address@hidden> wrote:
>  A quick comment: You need to specify the function for calculating the
>  Jacobian for sys-henon, the new implicit codes require it. Please look
>  at documentation in doc/ode-initval.texi. Use of fixed step size is
>  similar to old ode-initval.

Right.  Fixed version (with jacobian, attached below) seems to be working.

Actually, it works only for eps_abs ~ round off error.  Already for
eps_abs = 1e-10 it's easy to see small (linear?) drift in hamiltonian
from the constant.

Why mix step size control tolerances and root-finding tolerances?

Why not just use prefered fixed value of eps_abs for root-finding
(e.g.: GSL_DBL_EPSILON), as does attached patch for bug #30540 or
other implicit solvers (e.g.
http://www.unige.ch/~hairer/prog/stiff/radau5.f), but instead
complicate low level solver routines?

bug-ode2.c
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