Re: Parameter Optimization to match a PDE solution to experimental results

• To: mathgroup at smc.vnet.net
• Subject: [mg120986] Re: Parameter Optimization to match a PDE solution to experimental results
• From: Gabriel Landi <gtlandi at gmail.com>
• Date: Sat, 20 Aug 2011 06:17:47 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201108191032.GAA23915@smc.vnet.net>

```Check out the example in here
http://reference.wolfram.com/mathematica/ref/NonlinearModelFit.html
under the tab "Generalizations and Extensions".

The idea is that it is possible to fit data to a function which is not in analytic form.

Hope it helps.

Gabriel

On Aug 19, 2011, at 7:32 AM, Alexandre Santos Abreu wrote:

> Hello!
>
> I am new to Mathematica and want to know if my problem can be solved using it.
>
> I have a modified diffusion equation:
> dc/dt == D d^2c/dx^2 - rc exp(-n t)
>
> D: diffusion coefficient
> r: reaction rate
> c: concentration
> n: time constant
>
> What i need to do is finding the right parameter combination (D, r, n) in
> such a manner that the solution of the PDE corresponds to my experimental
> results. I already achieved numerical solving of the differential equation
> but i don't know if it is possible to use some fitting routine for the
> parameter optimization.
>
> I hope i described my problem clearly.
>
>
> Alex
>
>
> --
> Universit=E4t Augsburg
> Institut f=FCr Physik
> Lehrstuhl f=FCr Experimentalphysik II
> Universit=E4tsstr. 1
> 86159 Augsburg
>
> Tel.: 0821 598 3453
> Fax: 0821 598 3411
> e-mail: alexandre.abreu at physik.uni-augsburg.de
>

```

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