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[Help-gsl] odeiv2 rk2imp driver time step

From: Farkas, Illes
Subject: [Help-gsl] odeiv2 rk2imp driver time step
Date: Wed, 21 Dec 2011 14:07:51 -0800

Thanks, Tuomo

I just ran into something unexpected. I am trying to find out where exactly
I'm making a mistake.

I'm integrating with rk2imp a 3d ODE that has constants, linear and second
order polynomial terms on the r.h.s. I use gsl_odeiv2_driver_apply to
evolve the ODE in steps of 0.125s. After 10s or so (the exact time varies
with the parameters) all three variables converge (very little relative
change). However, some time ( > 5s ) later there is an update
when gsl_odeiv2_driver_apply returns the FAILURE value: -1. After logging
the current time directly from the "function" and "jacobian" (used by
the gsl_odeiv2_system, which is driver by the driver), I found that this
particular update fails, because the time step is halved again and again
until it reaches the limit of numerical precision.

Have you seen a similar error before ?

I have the Ascher Petzold book. Will sections 5.4.3 (modified Newton
iteration) and 4.7 (implicit methods) be helpful for this problem or shall
I use a different resource ?


2011/12/1 Tuomo Keskitalo <address@hidden>

> Hello,
> rk2imp (among other implicit methods) in ode-initval2 uses a modified
> Newton iteration instead of old functional iteration in solving the system
> of non-linear equations. E.g. for stiff problems Newton iteration is quite
> more powerful. Because of that, the ODE-solver can use larger step sizes.
> Newton iteration converges with larger step sizes, while functional
> iteration does not.
> On 12/01/2011 08:42 PM, Farkas, Illes wrote:
>  Hi,
>> I just tested the speed of rk2imp with the simple harmonic oscillator
>> (dx/dt=-y, dy/dt=x). In the first test I used
>> gsl_odeiv_step/control/evolve
>> (does *not* use Jacobian) and in the 2nd test I used
>> simply gsl_odeiv2_driver (uses Jacobian). With the same parameters the
>> first version ran for 26s and the second version finished below 1s. Is
>> this
>> test wrong? Or is there really such a big difference?
>> Thanks
>> Illes
>> ______________________________**_________________
>> Help-gsl mailing list
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