Re: fitting parameters to a differential equation
- To: mathgroup at smc.vnet.net
- Subject: [mg108436] Re: fitting parameters to a differential equation
- From: janos <janostothmeister at gmail.com>
- Date: Wed, 17 Mar 2010 04:42:16 -0500 (EST)
- References: <hnnk2g$cgs$1@smc.vnet.net>
On m=E1rc. 16, 10:46, eric g <eric.p... at gmail.com> wrote:
> Hello Group,
>
> does this make sense to you?:
>
> Suppose I have an second order differential equation on y[t]:
> y''+ay'+by=0, and I have a noise measurement of {y[t], @t1,t2,....tN}, I
> would like to fit 'a' and 'b' using the differential equation rather
> than using the solution.
>
> I will proceed like this:
>
> * take my y[t1],...,y[tN] measuremenst and do b-splines interpolation (I
> dont know what is the best way to do this), named yi[t], then find
> yi'[t], and yi''[t]
>
> * then I have an algebraic system on 'a,b' with N-equations (N is a big
> number) ayi'[t1]+by[t1]=-y''[t1],.....
>
> * how to use pseudoinverse to fit 'a' and 'b'? do you think this way may
> be better that a nonlinear fit (weighted nonlinear regression) using the
> solution of the equation? Do you think that this way may avoid the
> problem of finding the appropriate guess for the nonlinear fits
> algorithms with is ussually an issue?
>
> best regards,
> Eric
Eric,
You had better have a look at the Help of FindFit}Applications|
DifferentialEquations
Hope this helps,
J=E1nos