ODE IV Control and Variable Scale
Sat Mar 20 19:18:00 GMT 2010
about ODE solver error tolerances: you _never_ want to set eps_rel to
zero. It would mean that you allow no error for the ODE solver, which is
something no numerical method can give you.
As an example: gsl_odeiv_control_y_new (1e-12, 1e-8) means that if the
absolute value of a variable drops below 1e-12, you don't really care of
it's value any more (it is essentially zero for you). eps_rel = 1e-8
means that you want at least 7 decimals of each variable to be accurate
on each ODE solver step. If you need to control the level of error with
more detail, then you can use a_y, a_dydt and scale_abs.
A practical way to choose tolerances is to make a test and compare
results calculated with "strict" and "loose" eps_abs and eps_rel (order
of magnitude difference between strict and loose). If you get nearly
same values as result, you are probably safe to use your loose
tolerances. Of course, this depends on your problem, so be sure to test
it with your final computation case again.
If you are not interested in optimizing the performance, I'd suggest you
simply try to use control_y_new and see how it works for you.
On 03/18/2010 08:27 PM, Kevin H. Hobbs wrote:
> I'm trying make sure that I am using the gsl_odeiv_control functions
> I'm modelling neurons and my variables have different scales. Voltage is
> usually between -100 and 50 mV. The membrane current gating variables
> stay between 0 and 1. Internal calcium concentration is usually between
> 0 and a few hundred micro molar.
> Each time I read the descriptions of the gsl_odeiv_control functions I
> become more convinced that the parameters eps_rel, a_y, and a_dydt are
> there to excuse some error in variables and derivatives that are far
> from zero. Is that correct?
> Since I have no reason to care more about values close to zero (unless I
> do some complicated remapping of the variable values) should I set
> eps_rel, a_y, and a_dydt to 0?
> Since my variables have different ranges should I use
> gsl_odeiv_control_scaled_new with an appropriate eps_abs and scale_abs
> set with something like 1 for internal calcium concentration, 0.3 for
> membrane voltage, and 0.001 for all of the gating variables?
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