Re: [Boost-users] [Odeint] Stiff System of differential equations

Subject: Re: [Boost-users] [Odeint] Stiff System of differential equations
From: Karsten Ahnert (karsten.ahnert_at_[hidden])
Date: 2016-01-25 05:02:13

>> vector< double > obs_times = {
>>     0.0 , 0.1 , 0.2 , 0.3 , 0.4 , 0.5 , 0.6 , 0.7 , 0.8 , 0.9 , 1.0 };
>> double step_size = 0.02; // now it is really the initial step size
>> integrate_times(
>>     make_controlled< stepper >( abs_err , rel_err ) ,
>>     model2 , x , step_size , times.begin() , times.end() ,
>>     Print_observer );
> 
> I used integrate_times as you described above but it also froze after
> the .1 step. After having waited for a very long time I eventually get
> this error message
> """
> terminate called after throwing an instance of 'boost::exception_detail::clone_impl<boost::exception_detail::error_info_injector<std::overflow_error> >'
>  what():  Integrate adaptive : Maximal number of iterations reached. A step size could not be found.
> """

Might it be possible that you reached something like a singular point?
If the stepper does not find a step size it usually hints to some
problems with the ODE. Can you show me roughly your equations?

>> If you system is stiff you should also look at the Rosenbrock method. It
>> is much better suited for stiff problems. But its needs to calculate the
>> Jacobian.
>>
>>
> The biggest issue is that the Jacobian is too complicated to calculate,
> it depends on some population dynamics and higher order interpolation.
> 
> Is there no other way to solve stiff systems. I've read about other
> methods such as CVODE and LSODA, but couldn't figure out how to get
> those to work.

These methods exists but not within odeint and there are currently not
reachable from odeint. You might have a look at here:

https://computation.llnl.gov/casc/sundials/description/description.html