Re: lsode -- a do-it-all DGL solver?

[Thomas Treichl]

Matthias Brennwald schrieb:
> Dear all
>
> I'm not very much at home with the numerical theory behind solving 
> differential equations. Therefore my question: how do I decide which DGL 
> solver I should use? I have the impression that 'lsode' seems to be a 
> very advanced solver that is suitabe for most (all?) kinds of DGLs. Is 
> this correct? Also, how is it different from other solvers like ode23 or 
> ode45 (available in Matlab and Octave forge)? What are the 
> (dis)advantages of the different solvers?

Short summary:

  lsode() is extremely fast and therefore much faster then the solvers from 
octave-forge. lsode() is long term used and so very stable and also fits 
perfectly into Octave. You set options with the lsode_options() command in the 
background and don't need to pass options to the solver. The problem must be of 
the form x'=problem(x,t). Like John already told us you can solve non-stiff and 
stiff problems.

  odeXX() are slower in general - the core-solvers are long-term used but the 
interfaces to Octave are very young and therefore the one or other problem might 
appear. Some solvers can solve non-stiff problems others can solve non-stiff and 
stiff problems. Options are set in a Matlab compatible way with opt=odeset(). 
opt must be passed to the solver as the 4th argument then. The problem must of 
the form x'=problem(t,x).

  Thomas