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Re: Parameter Fitting in coupled differential equation

• To: mathgroup at smc.vnet.net
• Subject: [mg122367] Re: Parameter Fitting in coupled differential equation
• From: Oliver Ruebenkoenig <ruebenko at wolfram.com>
• Date: Wed, 26 Oct 2011 17:41:09 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201110251016.GAA05777@smc.vnet.net>

On Tue, 25 Oct 2011, Alexandre Santos Abreu wrote:

> Hello!
>
> I have two coupled differential equations:
>
> dx/dt = -(f2+r1) x + r2 y + f1 c0
> dy/dt = f2 cM x - f2 x y - r2 y
>
> As you can see I have five different parameters f1, f2, r1, r2, cM
> I also have two sets of measurements (x[t], y[t])
>
> Is it possible to let Mathematica search for the parameter set which
> produces the best fit to the measured values?
>
> Thanks!
>
> Alex
>
>

-- 

Here is I how I'd go about it. You could use NDSolve for the equations, 
extract the grid from the interpolation function (with if["Grid"]) then 
interpolate your measurement and evaluate on the NDSolve grid. Minimize 
the norm (in some sense) of the difference between the two.

Oliver

• References:
  • Parameter Fitting in coupled differential equation
    • From: "Alexandre Santos Abreu" <alexandre.abreu@physik.uni-augsburg.de>