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Least squares fit of a differential equation model

To: <s-news@lists.biostat.wustl.edu>
Subject: Least squares fit of a differential equation model
From: "Kogan, Clark" <clark.kogan@grizmail.umt.edu>
Date: Wed, 11 Jul 2007 11:28:32 -0600
Thread-index: AcfD4OeQT9HtnJ7aS7SycjxXkzTnmA==
Thread-topic: Least squares fit of a differential equation model
Hello,

I have a few questions related to using differential equation models.

I am going to be a little general, as I have different differential equation 
models that I may use.

Basically, I would like to do a least squares fit of data to a model consisting 
of a system of differential equations in order to determine the model 
parameters of best fit.

For instance, I might use the system: 
dy/dt = -k1x1 - k2x1x2
dx1/dt = k3y - k4x2
dx2/dt = k5y + k6x1

I would then collect data on y, x1, x2 at different times.

The goal in this situation would be to determine k1,k2,k3...

Are there any functions in S+, or functions that I could import into S+ that 
would work with differential equations in this manner.

Sorry if this is at all confusing, as I am still trying to understand it myself.
Thanks!

Clark Kogan

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