Re: ode23s, requested step-size too small

[Stephen Montgomery-Smith]

On 04/05/2013 11:54 AM, Torstein Fjermestad wrote:
> Dear all,
> 
> I am trying to solve a set of ordinary differential equations with ode23s.
> 
> In the output I get the following error message:
> 
> 
> 
> ode23s: requested step-size too small at t = 0, h = 4.65661e-10, err =
> -3.87203e-06
> ode23s: requested step-size too small at t = 0.000770534, h =
> -0.000766662, err = 4.49164e-23
> ode23s: requested step-size too small at t = 2.37561e-37, h =
> -4.2693e-37, err = -4.62411e-41
> ode23s: requested step-size too small at t = 6.73057e-48, h =
> 1.57155e-50, err = 3.98936e-47
> ode23s: requested step-size too small at t = 3.98936e-47, h =
> error: called from 'ode23s' in file
> /home/torstein/octave/odepkg-0.8.4/ode23s.m near line 193, column 10
> error: called from:
> error:   /usr/local/share/octave/3.6.4/m/miscellaneous/run.m at line 55,
> column 7
> 
> 
> I am calling the ode23s function in the following way:
> 
> 
> opt=odeset("InitialStep", 1e1,"RelTol", 1e-9, "AbsTol",
> 1e-12,"NormControl", "on","MaxStep",1e1);
> [vt,y]= ode23s(f,[0 endTime],Z0,opt);
> 
> Is there a way to get rid of the error message?
> 
> The problem I am trying to solve is a microkinetic analysis on a network
> of elementary reactions.
> The rate constants are in the range from 10^-7 to 10^12 so the system is
> quite stiff.

With the lsode command, you can also pass the Jacobian of f to the ode
solver, which might help.

Would you happen to know the eigenvalues of the Jacobian of f at t=0?
My impression is that most stiff solvers do well if the eigenvalues with
large absolute value are negative.  If these eigenvalues are close the
the imaginary axis (e.g. if any parts of the reaction are oscillating
extremely fast), then I don't think existing stiff solvers are of much
help.  Then I would be interested in working more closely with you to
solve your problem.  I have been working on these kinds of problems for
the last couple of years, and I would like to try the methods out in new
situations.