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From: Till on 4 Aug 2010 03:27
Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote in message <24770458.53299.1280905684888.JavaMail.root(a)gallium.mathforum.org>...
> > > Could you explain in more detail what you mean by
> > > 'use finite differences calculation to fit a
> > > curve' ?
> >
> >
> > Thank you for your answer Torsten and sorry for the
> > lack of specifity.
> > We are using simple finite differences calculation to
> > model diffusion in ceramic material because there is
> > no analytical solution available. If there was a
> > simple functional dependence I could use this
> > function in a non-linear least square fit with
> > results from diffusion experiments to obtain
> > parameters like the diffusion coefficient. But what I
> > need to do now is use this finite differences
> > calculation to fit the experimental results. After
> > the calculation basically end up with a two column
> > matrix with position and concentration of the
> > diffusing particle, which could be compared with the
> > experimental data. I would like to programm a fitting
> > procedure, which should then adjust the parameters in
> > a way, so that it converges the fit with the
> > experimental data. I was told there might be a chance
> > that this would be a bit more straight forward with
> > Matlab. So I wanted to check whether anybody
> > has experience with this.
> >
> > Best wishes,
> > Till
>
> You will have to couple an integrator which solves
> the diffusion equation with a nonlinear least-squares
> solver.
> In each iteration step, the nonlinear least-squares
> solver (e.g. LSQCURVEFIT) will supply a suggestion
> for the unknown parameters
> (e.g. the diffusion coefficient).
> With this suggestion, you can call a PDE-integrator
> (e.g. pdepe) to solve the diffusion equation to get
> the corresponding concentrations at the times when you measured your experimental data.
> Returning the array
> f_i = c_simulated(t_i) - c_experimental(t_i) (i=1,...,n)
> to the least-squares solver finishes the procedure.
>
> Best wishes
> Torsten.


Thank you very much. That is good information to start with.

Best Wishes,
Till
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