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From: Torsten Hennig <Torsten.Hennig@umsicht.fhg.de>
Newsgroups: comp.soft-sys.matlab
Subject: Re: simple parameter estimation
Date: Fri, 10 Oct 2008 12:08:51 EDT
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> Torsten Hennig <Torsten.Hennig@umsicht.fhg.de> wrote
> in message 
> > Now in your case an analytical solution for the 
> > above system of differential equations 
> > seems hard to determine.
> > 
> > For this reason, you have to couple ODE45 and one
> of the
> > parameter estimation routines:
> > 
> > In each step k, you get suggestions for parameters 
> > a_k, b_k, c_k from lsqnonlin or lsqcurvefit.
> > With these parameters, you call ODE45 to
> > determine the y_i(t_j,a_k,b_k,c_k) and transfer 
> > these values to lsqnonlin or lsqcurvefit.
> > In the next step, lsqnonlin or lsqcurvefit will 
> > transfer new a_(k+1), b_(k+1), c_(k+1).
> > You call ODE45 and so on.
> 
> Actually the problem I am trying to solve is pretty
> much harder than that, I guess it's about over 250
> equations, I mean, 250 differential equations and 248
> algebraic equations, 598 variables (of course), which
> gives us a differential-algebraic system of
> equations, which is, in that case, strictly
> non-linear. 
> Of course, I am trying to solve a simple ODE system
> before starting with a DAE system.
> 
> Ok, let me see whether I got your suggestion
> straight...
> You said to solve the system as albebraic and the
> result feeds the differential system and so on. I
> think I misunderstood something, will the results
> from the differential system feed a new algebraic
> system?
> 
> Thanks for commenting!


You should take a look at

http://num.math.uni-bayreuth.de/~kschittkowski/dyn_sys_book.htm

Here you get a reference to a book that will 
hopefully answer your questions.
 
A software-package called EASY-FIT is also 
available if the implementation in MATLAB is 
too time-consuming.

Best wishes
Torsten.